We need to develop a framework for discussing the benefits gained by society
through open trading in a free market. This idea is formally known as the
social efficiency or surplus. We’ll develop this idea in more detail in this
chapter with particular function on how we measure social surplus.
Social surplus alone is not the end of our discussion, we ideally want to relate
that to social welfare. Through a social welfare function, we can consider how
a surplus is distributed and whether that distribution is “just.” The social
welfare function may suggest that while total “raw” surplus is maximized by the
free market, this is not the optimal outcome from a social welfare perspective.
Social Efficiency or Surplus
Surplus is the idea that we derive additional benefits for certain trades and
smaller (but still positive) benefits from other trades. We break social surplus
into two parts: consumer surplus and producer surplus.
Consumer Surplus
Suppose you just finished a long hike and are extremely hungry. If I asked you
how much would you be willing to pay for a pizza slice, you might say $12 - you
are that hungry. You walk into the store and the buy a pizza slice for $1.50.
Even though you were willing to pay $12, you only paid $1.50. The difference
between these amounts is extra value that you realized. The $10.50 is your
surplus on that purchase.
We could repeat this process for each additional slice of pizza. Suppose your
willingness to pay per slice of pizza is given by the table:
| 1 |
12 |
1.50 |
10.50 |
| 2 |
8 |
1.50 |
6.50 |
| 3 |
4 |
1.50 |
2.50 |
| 4 |
2 |
1.50 |
0.50 |
| 5 |
1.50 |
1.50 |
0.00 |
We’d see your total surplus is
\[\text{surplus} = 10.50 + 6.50 + 2.50 + 0.50 + 0 = 20\]
In other words, for those 5 slices of pizza you would have been willing to pay
$27.50 but were only charged $7.50. The $20 of surplus was additional value
you realized above and beyond the amount you paid.
This idea - that trades where the willingness to pay exceeds the price are associated with additional value to the consumer - is the definition of the
consumer surplus.
You might realize that embedded in the earlier table is also the demand
schedule for pizza for our post-hike lunch.
The consumer surplus is then given by the difference between the demand curve
and the market price. Graphically, the area shaded in blue in Figure
4.1. The area above the price that clears the market and
below the demand line is part of the consumer surplus.
Note that the consumer surplus is represented as an area - it is the entire
surplus summed over each of the possible number of units consumed.
Producer Surplus
Just as with consumers, producers gain a surplus making trades. A firm can make
the first pizza slice for $0.50 but sells it for a $1.50. That difference
between the marginal cost of production and the market price represents a
surplus to the producer. As with the consumer, this varies by quantity Suppose
the second slice costs $0.90 to make, then the surplus to the producer is only
$0.60, not $1.00.
As you might expect, the producer surplus is then the additional profit that a producer realizes when MC is lower than the market price. This can be shown
graphically as the area below the market price line but above the supply
curve, Figure ??.
Total Social Surplus
The total social surplus is simply the sum of the producer and consumer surplus.
This sum is the total additional value to society as a result of the trades
made in this market.
Total Social Surplus is Maximized at the Competitive Equilibirum
The total social surplus is greatest at the competitive equilibrium.
When the market is at the competitive equilibrium, no trades are possible that
have a net positive benefit (either both parties are better off or at least
one party is unharmed while the other party is better off). In other words,
all trades that are possible within the costs and budgets of consumers or
the production and cost functions of producers have occurred. If consumers
bought an additional unit at the price suppliers demand, they would have a net
negative value (bought for more than they valued the good). If producers sold
one more at the price consumers are willing to pay, they would be losing money
on the trade. Since no trades
are possible that make consumers or producers better off, any additional
trades must reduce either consumer or producer social surplus and, by extension,
total social surplus.
If the market is not at the competitive equilibrium, there are trades that are
still possible that would increase either consumer utility without exceeding the
budget and at prices producers are willing to offer or increase profit for the
firm. This leads to the First Fundamental Theorem of Welfare Economics:
total social surplus or social efficiency is maximized at the competitive equilibrium.
Any policy that causes a deviation from the competitive equilibrium comes at
the cost of reducing total social surplus. We’ll consider three polices that
would cause the market to deviate from the competitive equilibrium and see how
they affect consumer, producer, and social surplus.
Quantity Control
Cities and governments often use policy controls, especially through zoning and
permitting, to control the supply of particular goods. For instance, the City of
Iowa City recently was interested in “reclaiming” and “preserving” the
owner-occupied single-family homes near downtown Iowa City. Many of these homes
over the years have been subdivided into rental properties. This has the effect
of changing the character of the area with a greater number of student renters
and fewer families. More importantly, being able to subdivide and rent the
houses out drove up the price of the houses. Someone buying the house to live
in it would need to pay the same or more than someone interested in buying the
house to convert into a rental.
The City of Iowa City decided to respond by creating a cap on the number of
rental permits that would be issued by neighborhood. They refused to issue new
rental permits in neighborhoods with greater than some threshold of rental
properties (e.g., if more than 30% of houses were rentals, they would not issue
a permit for a new rental). This
had the effect of restricting supply of rental housing to a certain upper
limit.
We can model the effect of this policy by adjusting our supply curve.
Specifically, once we hit a certain quantity, the supply curve becomes a
verticle line - no matter how much the price increases, there will be no
quantity permitted above the cap created by the quantity control.
Suppose before we apply the cap, we have the market in the panel of
Figure 4.4 labeled “Before Quantity Restriction.” This shows
the market’s behavior before the policy restricting the quantity supplied.
At this point, there will be 100 units of the good traded at a price of
$1,500.
The government deems this outcome to be unacceptable and instead restricts
the number of trades allowed to 75. This would be similar to the rental cap
passed by Iowa City. This change is shown as the dashed red line in the
panel of Figure 4.4 labeled “With Quantity Restriction.”
With the cap in place, only 75 trades can be made and the equilibrium must
shift. The new equilibrium (denoted QR for Quantity Restricted in Figure
4.4) still takes place at the intersection of the supply
and demand curves. Since demand is unaffected, the price that clears the market
will be higher than at the competitive equilibrium ($2,401.67).
Because the market price shifted, we also need to redraw the consumer and
producer surplus. It is still given by the area between the demand line and the
price (consumer surplus) or the supply line and the price (producer surplus).
You’ll note that some of the region that was previously consumer surplus is
now producer surplus because of the increased price. The percentage of the total
surplus that goes to producers has increased at the expense of the share going
to consumers.
Meanwhile, the total social surplus has decreased. The new supply line reflects
an imposed constraint on the market and prevents parties from making mutually
beneficial trades. Before the restriction, suppliers were happy to sell the
25 additional goods at lower prices; however, they are prevented from doing
so. As a result, society has to forgo these trades. We label the lost
value of these trades as the dead weight loss of the policy. The dead
weight loss is the area between the supply and demand lines, before the
policy, for quantity above \(Q_\text{QR}\).
Rent Control
A policy commonly mentioned as a way to control housing costs is rent control.
Under a rent control program, the rent charged for a housing unit is restricted
to some maximum level. This has the effect of transforming the supply line into
a horizontal line once the price equals the threshold price defined by the
policy. No matter how many units are offered, suppliers cannot charge a rent
above the cap.
Figure 4.5 shows such a market. Before a rent control
policy, a total of 100 units were rented out at a market price of $1,500. This
is shown in the panel labeled “Before Rent Control.” A rent control policy
was enacted, limiting the maximum rent landlords could charge to $1,050.
The new equilibrium shifts to the point labeled RC (rent control). Since the
marginal cost for landlords to rent out more than 75 units is greater than the
price they can charge in rent, the supply curve becomes flat. Landlords are
only willing to provide 75 units. Compared to the point CE, at RC, the
rent is reduced by $450 but there are 25 fewer units open to be rented.
As with the quantity restriction, there are changes in the consumer and
producer surplus. The consumer surplus, as a share of the total surplus,
increases to reflect the new lower price. However, the total social surplus
is reduced by the dead weight loss (the green area in Figure 4.5).
Taxes
Rent control and quantity restrictions are brute force interventions. The
government also has the option of taxing a good they wish to discourage.
A tax would reduce supply since it would increase the cost of production
above the bare marginal cost.
One common excise or sin tax is a tax on tobacco products. The government wants
to discourage smoking and uses higher taxes to do so. Suppose the government
applies a 25% tax to all tobacco products. The market may look something like
Figure 4.6. The resulting figure is somewhat more complicated.
The equilibrium shifts from CE to TE (tax equilibrium) with an increase in
price and decrease in the quantity traded. The consumer surplus is the region
above the new market price (\(P_\text{TE}\)) and below the demand line. The
producer surplus is the region below the value of the original supply curve
at \(Q_\text{TE}\). This reduction is the result of the tax with the value of the
tax shown as the region in gold between the producer and consumer surplus. The
dead weight loss is highlighted in green and shows the loss of surplus due to
forgoing those trades.
Social Welfare
The competitive equilibrium maximizes social surplus but social surplus is
not the be-all, end-all. We might find that the particular distribution of
surplus and goods at competitive equilibrium does not match what we want in a
just society. We might want to place our “thumb on the scale” to favor a
different outcome that is more “just” or “fair” than that offered by just the
free market.
This highlights an limitation of the first fundamental theorem of welfare
economics. It is possible for the Pareto efficient, competitive equilibrium
to be undesirably from a social point of view. For instance, nothing in the
first fundamental theorem would have issue with one person owning everything
and everyone else having nothing so long as that outcome was Pareto efficient.
The Second Fundamental Theorem of Welfare Economics says that we can
reach a socially more desirable outcome by redistributing resources and then
allowing the market to guide the outcome. In practice, this redistribution of
resources is hard politically and also will almost certainly create some degree
of inefficiency.
We generally “put our thumb on the scale” using different approaches then
pure redistribution. However, when we do this, we almost always arrive at an
equilibrium point that is less efficient than the free market competitive
equilibrium. We have a trade-off to consider between the social surplus and the
overall fairness of our outcome.
We describe this trade-off between efficiency and equity using a social welfare
function (SWF). The social welfare function will guide us when determining
when and to what extent we want to put our thumb on the scale. We’ll consider
two common social welfare functions in this class: utilitarian and Rawlsian
social welfare functions.
Utilitarian SWF
The utilitarian social welfare function stems from the philosophy of utilitarianism
developed by the philosopher Jeremy Bentham Utilitarianism as a philosophy, simply put, is the idea that we
should make the choices that leave the affected parties the most happiest and
to maximize well-being.
As a result of this, the utilitarian social welfare function says that we should prefer changes that increase the total utility in society. In other words, we
should not focus on how individual people are affected by a policy but rather
how the whole of society is changed.
As a general case, we would say the utilitarian social welfare function is,
in a society with \(k\) people,
\[\text{SWF}_u = U_1 + U_2 + U_3 + \ldots + U_k\]
where \(U_i\) is the utility of the \(i^\text{th}\) person. Alternatively, we could
express this using summation notation as
\[\text{SWF}_u = \sum_{i = 1}^k U_i\]
For instance, suppose our society has three people: Bill, Ted, and Rufus. We
have some current state of affairs will Bill has 100 utility units, Ted has
50, and Rufus has 10. Our total level of utility across all society is then
\(100 + 50 + 10 = 160\).
To determine if a new outcome is more or less just, we consider how the total
utility over all members of society changes with the new policy. Suppose we
pass a tax that transfers income from the highest earners to the lowest
earning members in our society (e.g., from Bill to Rufus). Because of the
property of diminishing marginal utility, it is likely that the harm to Bill’s
utility will be smaller than the benefit to Rufus’s. After the tax and transfer,
we have Bill having 95 utility units, Ted having 50, and Rufus having 20. The
total utility in society is \(95 + 50 + 20 = 165\), or 5 more than before the
tax and transfer. Therefore, a utilitarian social welfare function would prefer
this state.
Conversely, suppose we had a tax and transfer scheme the other way: Rufus
paid the tax and Bill benefited. Let’s say that Rufus lost 5 utility
units of income to the tax and Bill got 2.5 units of extra utility. We then
have a situation where total utility is \(102.5 + 50 + 5 = 157.5\), or 2.5
units lower than the baseline. Based on the utilitarian social welfare function,
we would not prefer this outcome.
Note that the utilitarian social welfare function is not sensitive to the
distribution of utility. Suppose we took all of the utility away from Rufus and
Ted and transferred it all to Bill. We now have Bill having 160 utility points
while Ted and Rufus have none. Based on the social welfare function, this
outcome is just as good as the one where Bill had 100, Bill had 50, and Rufus
had 10.
Rawlsian SWF
While the utilitarian social welfare function often leads to the right
decision for a society, it does have drawbacks due to its lack of distributional
sensitivity. The Rawlsian social welfare function, derived from the arguments
made by the American philosopher John Rawls, addresses that shortcoming.
Rawls argued that we should be chiefly concerned with how the least well off
member of society is affected by a policy. He argued for using a social welfare
function that has as its value the lowest utility of all members on society.
Formally,
\[\text{SWF}_R = \min(U_1, U_2, U_3, \ldots, U_k)\]
This is attractive because we are often most concerned with how a policy might
impact the least well off and so having a social welfare function that
centers on that idea is useful. This is different from the utilitarian social
welfare function in that the total utility in society can decrease but that
new situation may still be preferred if the lowest utility was increased.
With our examples above, the Rawlsian social welfare function is supportive of
a policy that transfers income from Bill to Rufus as Rufus’s utility is
increased. This would remain true even if the decrease in Bill’s utility was
greater than the increase in Rufus’s.
When we consider the extreme example of a policy that changes utility to
160 for Bill and zero for both Ted and Rufus, the Rawlsian social welfare
function would reject this outcome as being equally “good” as the baseline.
The lowest utility has changed from 10 (Rufus) to 0 (Ted or Rufus) and so the
policy would not be preferred.
A Rawlsian social welfare function is not immune to pathology. In particular,
society can be clearly worse off but if the least member is improved, then
that policy is preferred. For instance, suppose Bill earns $100,000 while Rufus
earns $5,000. If we take $50,000 from Bill and give $1 to Rufus and burn
the $49,999 that remain, a Rawlsian social welfare function would prefer this
alternative. This outcome is clearly not desirable and wastes a considerable
amount of utility by burning $49,999 but because Rufus is $1 richer, it is
better.
Applying a SWF
In practice, you would rarely want to decide to only use a Rawlsian or a
utilitarian social welfare function. Both have strengths but also significant
weaknesses. The lack of attention to distribution of the utility in a utilitarian
setting is a major weakness - distribution matters - but reducing that measure
to only how the worst off is doing likely distorts decision making by an equal
amount. You would likely want to consider and weigh the decision using both
social welfare functions, adding a slight bias towards one or another depending
on the question.
Consideration of the question is critical. There are some questions where we
clearly would be very interested in how the least well off person is doing.
For instance, with health care, which we feel is important to health and a
human right, is a case where we might prefer the decisions closer to those
made with the Rawlsian social welfare function. Since we are concerned with how
all people are doing, we are particularly concerned with how the worst off is
doing.
But other questions are less compelling. If we were considering access to LASIK
eye surgery as opposed to regular health care and access to adequate vision care.
We would want everyone to be able to see and might use a Rawlsian social
welfare function when considering access to adequate vision care, but we don’t
feel as though using glasses or contacts is so burdensome that we really care
that everyone can get LASIK. We would likely use a utilitarian framework to
understand policies related to access or reducing the barriers to access to
optical care like LASIK.
As a general matter, the Rawlsian SWF will prefer
more redistribution of resources while the utilitarian SWF will prefer somewhat
less.
Equity Criterion
Governments and society do not only use the desire to obtain social surplus or
the results of the social welfare function to identify their goals. They also
use an equity criterion when determining whether to intervene. Two equity
criteria are in common use.
The first, called commodity egalitarianism, states that after baseline needs are
met, income and utility inequality are not relevant. For instance, once the
government has ensured that each citizen reaches a minimally acceptable standard
of living, how much people earn does not matter. Suppose that it costs $50,000
to live in a city and the city has three residents - Jane who earns $1,000,000,
Elizabeth who earns $100,000, and Mary who earns $50,000. The incomes are
highly unequal but all three have enough to live comfortable and intervention
or redistribution is not indicated. However, if Mary earned $40,000 then
intervention to redistribute resources would be indicated.
The second commonly used criterion is equality of opportunity. Under this
standard, the government should ensure all citizens have an equal change of
success but has no role in determining who succeeds or who fails. Intervention
to alter outcomes after ensuring equality of opportunity is beyond the proper
scope of the government.
Chapter 4 Social Efficiency and Welfare
We need to develop a framework for discussing the benefits gained by society through open trading in a free market. This idea is formally known as the social efficiency or surplus. We’ll develop this idea in more detail in this chapter with particular function on how we measure social surplus.
Social surplus alone is not the end of our discussion, we ideally want to relate that to social welfare. Through a social welfare function, we can consider how a surplus is distributed and whether that distribution is “just.” The social welfare function may suggest that while total “raw” surplus is maximized by the free market, this is not the optimal outcome from a social welfare perspective.
4.1 Social Efficiency or Surplus
Surplus is the idea that we derive additional benefits for certain trades and smaller (but still positive) benefits from other trades. We break social surplus into two parts: consumer surplus and producer surplus.
4.1.1 Consumer Surplus
Suppose you just finished a long hike and are extremely hungry. If I asked you how much would you be willing to pay for a pizza slice, you might say $12 - you are that hungry. You walk into the store and the buy a pizza slice for $1.50.18 Even though you were willing to pay $12, you only paid $1.50. The difference between these amounts is extra value that you realized. The $10.50 is your surplus on that purchase.
We could repeat this process for each additional slice of pizza. Suppose your willingness to pay per slice of pizza is given by the table:
We’d see your total surplus is
\[\text{surplus} = 10.50 + 6.50 + 2.50 + 0.50 + 0 = 20\]
In other words, for those 5 slices of pizza you would have been willing to pay $27.50 but were only charged $7.50. The $20 of surplus was additional value you realized above and beyond the amount you paid.
This idea - that trades where the willingness to pay exceeds the price are associated with additional value to the consumer - is the definition of the consumer surplus.
You might realize that embedded in the earlier table is also the demand schedule for pizza for our post-hike lunch.
The consumer surplus is then given by the difference between the demand curve and the market price. Graphically, the area shaded in blue in Figure 4.1. The area above the price that clears the market and below the demand line is part of the consumer surplus.
Figure 4.1: Demand Curve, Market Price, and Consumer Surplus. The demand curve is shown in blue and is downward sloping while the market price, or the price charged to consume, is flat (dashed black line). The difference between these two lines is the consumer surplus. We repersent that as the area shaded in blue.
Note that the consumer surplus is represented as an area - it is the entire surplus summed over each of the possible number of units consumed.
4.1.2 Producer Surplus
Just as with consumers, producers gain a surplus making trades. A firm can make the first pizza slice for $0.50 but sells it for a $1.50. That difference between the marginal cost of production and the market price represents a surplus to the producer. As with the consumer, this varies by quantity Suppose the second slice costs $0.90 to make, then the surplus to the producer is only $0.60, not $1.00.
As you might expect, the producer surplus is then the additional profit that a producer realizes when MC is lower than the market price. This can be shown graphically as the area below the market price line but above the supply curve, Figure ??.
Figure 4.2: Supply Curve, Market Price, and Producer Surplus. The supply curve is shown in red and is upward sloping while the market price, or the price paid by the consumer, is flat (dashed black line). The difference between these two lines is the producer surplus. We repersent that as the area shaded red.
4.2 Total Social Surplus
The total social surplus is simply the sum of the producer and consumer surplus. This sum is the total additional value to society as a result of the trades made in this market.
Figure 4.3: Supply, Demand, and Surplus. The sum of the red and blue shaded areas is the total social surplus in this market.
4.2.1 Total Social Surplus is Maximized at the Competitive Equilibirum
The total social surplus is greatest at the competitive equilibrium. When the market is at the competitive equilibrium, no trades are possible that have a net positive benefit (either both parties are better off or at least one party is unharmed while the other party is better off). In other words, all trades that are possible within the costs and budgets of consumers or the production and cost functions of producers have occurred. If consumers bought an additional unit at the price suppliers demand, they would have a net negative value (bought for more than they valued the good). If producers sold one more at the price consumers are willing to pay, they would be losing money on the trade. Since no trades are possible that make consumers or producers better off, any additional trades must reduce either consumer or producer social surplus and, by extension, total social surplus.
If the market is not at the competitive equilibrium, there are trades that are still possible that would increase either consumer utility without exceeding the budget and at prices producers are willing to offer or increase profit for the firm. This leads to the First Fundamental Theorem of Welfare Economics: total social surplus or social efficiency is maximized at the competitive equilibrium.
Any policy that causes a deviation from the competitive equilibrium comes at the cost of reducing total social surplus. We’ll consider three polices that would cause the market to deviate from the competitive equilibrium and see how they affect consumer, producer, and social surplus.
4.2.1.1 Quantity Control
Cities and governments often use policy controls, especially through zoning and permitting, to control the supply of particular goods. For instance, the City of Iowa City recently was interested in “reclaiming” and “preserving” the owner-occupied single-family homes near downtown Iowa City. Many of these homes over the years have been subdivided into rental properties. This has the effect of changing the character of the area with a greater number of student renters and fewer families. More importantly, being able to subdivide and rent the houses out drove up the price of the houses. Someone buying the house to live in it would need to pay the same or more than someone interested in buying the house to convert into a rental.
The City of Iowa City decided to respond by creating a cap on the number of rental permits that would be issued by neighborhood. They refused to issue new rental permits in neighborhoods with greater than some threshold of rental properties (e.g., if more than 30% of houses were rentals, they would not issue a permit for a new rental).19 This had the effect of restricting supply of rental housing to a certain upper limit.
We can model the effect of this policy by adjusting our supply curve. Specifically, once we hit a certain quantity, the supply curve becomes a verticle line - no matter how much the price increases, there will be no quantity permitted above the cap created by the quantity control.
Suppose before we apply the cap, we have the market in the panel of Figure 4.4 labeled “Before Quantity Restriction.” This shows the market’s behavior before the policy restricting the quantity supplied. At this point, there will be 100 units of the good traded at a price of $1,500.
The government deems this outcome to be unacceptable and instead restricts the number of trades allowed to 75. This would be similar to the rental cap passed by Iowa City. This change is shown as the dashed red line in the panel of Figure 4.4 labeled “With Quantity Restriction.” With the cap in place, only 75 trades can be made and the equilibrium must shift. The new equilibrium (denoted QR for Quantity Restricted in Figure 4.4) still takes place at the intersection of the supply and demand curves. Since demand is unaffected, the price that clears the market will be higher than at the competitive equilibrium ($2,401.67).
Figure 4.4: Effect of a Quantity Restriction on a Market. The new supply line after the cap is shown as the dashed red line. The consumer and producer surplus changes to reflect the new market price. The area shaded in green in the dead weight loss of the policy.
Because the market price shifted, we also need to redraw the consumer and producer surplus. It is still given by the area between the demand line and the price (consumer surplus) or the supply line and the price (producer surplus). You’ll note that some of the region that was previously consumer surplus is now producer surplus because of the increased price. The percentage of the total surplus that goes to producers has increased at the expense of the share going to consumers.
Meanwhile, the total social surplus has decreased. The new supply line reflects an imposed constraint on the market and prevents parties from making mutually beneficial trades. Before the restriction, suppliers were happy to sell the 25 additional goods at lower prices; however, they are prevented from doing so. As a result, society has to forgo these trades. We label the lost value of these trades as the dead weight loss of the policy. The dead weight loss is the area between the supply and demand lines, before the policy, for quantity above \(Q_\text{QR}\).
4.2.1.2 Rent Control
A policy commonly mentioned as a way to control housing costs is rent control. Under a rent control program, the rent charged for a housing unit is restricted to some maximum level. This has the effect of transforming the supply line into a horizontal line once the price equals the threshold price defined by the policy. No matter how many units are offered, suppliers cannot charge a rent above the cap.
Figure 4.5 shows such a market. Before a rent control policy, a total of 100 units were rented out at a market price of $1,500. This is shown in the panel labeled “Before Rent Control.” A rent control policy was enacted, limiting the maximum rent landlords could charge to $1,050. The new equilibrium shifts to the point labeled RC (rent control). Since the marginal cost for landlords to rent out more than 75 units is greater than the price they can charge in rent, the supply curve becomes flat. Landlords are only willing to provide 75 units. Compared to the point CE, at RC, the rent is reduced by $450 but there are 25 fewer units open to be rented.
Figure 4.5: Effect of Rent Control on a Market. The new supply line after the rent control policy is shown as the dashed red line. The consumer and producer surplus changes to reflect the new market price. The area shaded in green in the dead weight loss of the policy.
As with the quantity restriction, there are changes in the consumer and producer surplus. The consumer surplus, as a share of the total surplus, increases to reflect the new lower price. However, the total social surplus is reduced by the dead weight loss (the green area in Figure 4.5).
4.2.1.3 Taxes
Rent control and quantity restrictions are brute force interventions. The government also has the option of taxing a good they wish to discourage. A tax would reduce supply since it would increase the cost of production above the bare marginal cost.
One common excise or sin tax is a tax on tobacco products. The government wants to discourage smoking and uses higher taxes to do so. Suppose the government applies a 25% tax to all tobacco products. The market may look something like Figure 4.6. The resulting figure is somewhat more complicated.
Figure 4.6: Effect of a Tax on Tobacco Production. The demand line after the production tax is shown as the dotted red line. The equilibirum points under taxation and free market conditions are labeled TE and CE, respectively. The shaded blue region is the consumer surplus, the shaded red region is the producer surplus, the gold region is the value of the tax, and the green region is the dead weight loss.
The equilibrium shifts from CE to TE (tax equilibrium) with an increase in price and decrease in the quantity traded. The consumer surplus is the region above the new market price (\(P_\text{TE}\)) and below the demand line. The producer surplus is the region below the value of the original supply curve at \(Q_\text{TE}\). This reduction is the result of the tax with the value of the tax shown as the region in gold between the producer and consumer surplus. The dead weight loss is highlighted in green and shows the loss of surplus due to forgoing those trades.
4.3 Social Welfare
The competitive equilibrium maximizes social surplus but social surplus is not the be-all, end-all. We might find that the particular distribution of surplus and goods at competitive equilibrium does not match what we want in a just society. We might want to place our “thumb on the scale” to favor a different outcome that is more “just” or “fair” than that offered by just the free market.
This highlights an limitation of the first fundamental theorem of welfare economics. It is possible for the Pareto efficient, competitive equilibrium to be undesirably from a social point of view. For instance, nothing in the first fundamental theorem would have issue with one person owning everything and everyone else having nothing so long as that outcome was Pareto efficient.
The Second Fundamental Theorem of Welfare Economics says that we can reach a socially more desirable outcome by redistributing resources and then allowing the market to guide the outcome. In practice, this redistribution of resources is hard politically and also will almost certainly create some degree of inefficiency.
We generally “put our thumb on the scale” using different approaches then pure redistribution. However, when we do this, we almost always arrive at an equilibrium point that is less efficient than the free market competitive equilibrium. We have a trade-off to consider between the social surplus and the overall fairness of our outcome.
We describe this trade-off between efficiency and equity using a social welfare function (SWF). The social welfare function will guide us when determining when and to what extent we want to put our thumb on the scale. We’ll consider two common social welfare functions in this class: utilitarian and Rawlsian social welfare functions.
4.3.1 Utilitarian SWF
The utilitarian social welfare function stems from the philosophy of utilitarianism developed by the philosopher Jeremy Bentham20 Utilitarianism as a philosophy, simply put, is the idea that we should make the choices that leave the affected parties the most happiest and to maximize well-being.
As a result of this, the utilitarian social welfare function says that we should prefer changes that increase the total utility in society. In other words, we should not focus on how individual people are affected by a policy but rather how the whole of society is changed.
As a general case, we would say the utilitarian social welfare function is, in a society with \(k\) people,
\[\text{SWF}_u = U_1 + U_2 + U_3 + \ldots + U_k\]
where \(U_i\) is the utility of the \(i^\text{th}\) person. Alternatively, we could express this using summation notation as
\[\text{SWF}_u = \sum_{i = 1}^k U_i\]
For instance, suppose our society has three people: Bill, Ted, and Rufus. We have some current state of affairs will Bill has 100 utility units, Ted has 50, and Rufus has 10. Our total level of utility across all society is then \(100 + 50 + 10 = 160\).
To determine if a new outcome is more or less just, we consider how the total utility over all members of society changes with the new policy. Suppose we pass a tax that transfers income from the highest earners to the lowest earning members in our society (e.g., from Bill to Rufus). Because of the property of diminishing marginal utility, it is likely that the harm to Bill’s utility will be smaller than the benefit to Rufus’s. After the tax and transfer, we have Bill having 95 utility units, Ted having 50, and Rufus having 20. The total utility in society is \(95 + 50 + 20 = 165\), or 5 more than before the tax and transfer. Therefore, a utilitarian social welfare function would prefer this state.
Conversely, suppose we had a tax and transfer scheme the other way: Rufus paid the tax and Bill benefited.21 Let’s say that Rufus lost 5 utility units of income to the tax and Bill got 2.5 units of extra utility. We then have a situation where total utility is \(102.5 + 50 + 5 = 157.5\), or 2.5 units lower than the baseline. Based on the utilitarian social welfare function, we would not prefer this outcome.
Note that the utilitarian social welfare function is not sensitive to the distribution of utility. Suppose we took all of the utility away from Rufus and Ted and transferred it all to Bill. We now have Bill having 160 utility points while Ted and Rufus have none. Based on the social welfare function, this outcome is just as good as the one where Bill had 100, Bill had 50, and Rufus had 10.
4.3.2 Rawlsian SWF
While the utilitarian social welfare function often leads to the right decision for a society, it does have drawbacks due to its lack of distributional sensitivity. The Rawlsian social welfare function, derived from the arguments made by the American philosopher John Rawls, addresses that shortcoming.
Rawls argued that we should be chiefly concerned with how the least well off member of society is affected by a policy. He argued for using a social welfare function that has as its value the lowest utility of all members on society. Formally,
\[\text{SWF}_R = \min(U_1, U_2, U_3, \ldots, U_k)\]
This is attractive because we are often most concerned with how a policy might impact the least well off and so having a social welfare function that centers on that idea is useful. This is different from the utilitarian social welfare function in that the total utility in society can decrease but that new situation may still be preferred if the lowest utility was increased.
With our examples above, the Rawlsian social welfare function is supportive of a policy that transfers income from Bill to Rufus as Rufus’s utility is increased. This would remain true even if the decrease in Bill’s utility was greater than the increase in Rufus’s.
When we consider the extreme example of a policy that changes utility to 160 for Bill and zero for both Ted and Rufus, the Rawlsian social welfare function would reject this outcome as being equally “good” as the baseline. The lowest utility has changed from 10 (Rufus) to 0 (Ted or Rufus) and so the policy would not be preferred.
A Rawlsian social welfare function is not immune to pathology. In particular, society can be clearly worse off but if the least member is improved, then that policy is preferred. For instance, suppose Bill earns $100,000 while Rufus earns $5,000. If we take $50,000 from Bill and give $1 to Rufus and burn the $49,999 that remain, a Rawlsian social welfare function would prefer this alternative. This outcome is clearly not desirable and wastes a considerable amount of utility by burning $49,999 but because Rufus is $1 richer, it is better.
4.3.3 Applying a SWF
In practice, you would rarely want to decide to only use a Rawlsian or a utilitarian social welfare function. Both have strengths but also significant weaknesses. The lack of attention to distribution of the utility in a utilitarian setting is a major weakness - distribution matters - but reducing that measure to only how the worst off is doing likely distorts decision making by an equal amount. You would likely want to consider and weigh the decision using both social welfare functions, adding a slight bias towards one or another depending on the question.
Consideration of the question is critical. There are some questions where we clearly would be very interested in how the least well off person is doing. For instance, with health care, which we feel is important to health and a human right, is a case where we might prefer the decisions closer to those made with the Rawlsian social welfare function. Since we are concerned with how all people are doing, we are particularly concerned with how the worst off is doing.
But other questions are less compelling. If we were considering access to LASIK eye surgery as opposed to regular health care and access to adequate vision care. We would want everyone to be able to see and might use a Rawlsian social welfare function when considering access to adequate vision care, but we don’t feel as though using glasses or contacts is so burdensome that we really care that everyone can get LASIK. We would likely use a utilitarian framework to understand policies related to access or reducing the barriers to access to optical care like LASIK.
As a general matter, the Rawlsian SWF will prefer more redistribution of resources while the utilitarian SWF will prefer somewhat less.
4.4 Equity Criterion
Governments and society do not only use the desire to obtain social surplus or the results of the social welfare function to identify their goals. They also use an equity criterion when determining whether to intervene. Two equity criteria are in common use.
The first, called commodity egalitarianism, states that after baseline needs are met, income and utility inequality are not relevant. For instance, once the government has ensured that each citizen reaches a minimally acceptable standard of living, how much people earn does not matter. Suppose that it costs $50,000 to live in a city and the city has three residents - Jane who earns $1,000,000, Elizabeth who earns $100,000, and Mary who earns $50,000. The incomes are highly unequal but all three have enough to live comfortable and intervention or redistribution is not indicated. However, if Mary earned $40,000 then intervention to redistribute resources would be indicated.
The second commonly used criterion is equality of opportunity. Under this standard, the government should ensure all citizens have an equal change of success but has no role in determining who succeeds or who fails. Intervention to alter outcomes after ensuring equality of opportunity is beyond the proper scope of the government.