Gains From Exchange (Trade) and Effects of Government Policies

Measuring the Gains from Exchange Whenever an exchange (or trade) takes place between a consumer and a producer, both parties gain from that exchange (or trade) The consumer’s gain from the exchange is termed as – The consumer’s surplus The producer’s gain from the exchange is termed as – The producer’s surplus The sum of the consumer’s and producer’s surplus is the total gains from a particular exchange (or trade).

Consumer’s Surplus Consumer’s surplus (CS) is the monetary difference between the maximum amount that a consumer is willing to pay for the quantity purchased and what the good actually costs. Step function

Marginal Value and Demand Marginal Value: The maximum amount a consumer would be willing to pay to acquire an additional unit of a good – Marginal value curve and demand curve convey similar information Application of equi-marginal principle – Buy the good as long as marginal value exceeds the price – The consumer is in equilibrium where marginal value equals the price Total Value: The maximum amount a consumer would be willing to pay to acquire a given quantity of a good.

A Numerical Example QuantityPriceWilling to Pay Actual Payment Consumer Surplus

Marginal and Total Value

The Consumer’s Surplus

Market Consumer Surplus Market demand is the (horizontal) sum of individual demand curves; market CS is the sum of each individual consumer’s surplus. CS losses following a price increase are larger: the greater the initial revenue (p∙Q) spent on the good the less elastic the demand curve at equilibrium

Effect of a 10% Price Increase on Consumer Surplus Revenue and Consumer Surplus in Billions of 2008 Dollars

Graphically Deriving A Consumer’s Demand Curve Allowing the price of the good on the x-axis to fall, the budget constraint rotates out and shows how the optimal quantity of the x-axis good purchased increases. This traces out points along the demand curve.

Consumer’s Surplus Consumer’s surplus (CS) is the area under the inverse demand curve and above the market price up to the quantity purchased by the consumer. Smooth inverse demand function

Effect of a Price Change on Consumer’s Surplus If the price of a good rises (e.g. £0.50 to £1), purchasers of that good lose consumer’s surplus (falls by A + B) This is the amount of income we would have to give the consumer to offset the harm of an increase in price.

Consumer’s Surplus: A Mathematical Application Suppose that the demand function of a consumer is given by Q D = 40 – 2P. If the market price P = 10, what is the consumer’s surplus? Given the market price P = 10, a consumer’s quantity demanded Q D = 40 – 2P = 40 – 2*10 = 20 The consumer’s surplus is the area of the triangle between the price line and the inverse demand curve The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 10 = 10. CS = ½ (20*10) = 100 If the market price falls to P = 5, how the consumer’s surplus would change? Given the market price P = 5, a consumer’s quantity demanded Q D = 40 – 2P = 40 – 2*5 = 30 So the consumer’s surplus (the area of the triangle between the price line and the inverse demand curve) is CS = ½ (30*15) = 225 (because the height of the triangle is 20 – 5 = 15) The change in consumer’s surplus, ∆CS = 225 – 100 = 125

The Producer’s Surplus The Producer’s Surplus is defined as the dollar amount by which a firm benefits by producing its profit maximizing level of output. In other words, a Producer’s Surplus is the amount by which the producer’s revenue exceeds her variable production costs

The Producer’s Surplus

Producer Surplus Producer surplus (PS) is the difference between the amount for which a good sells (market price) and the minimum amount necessary for sellers to be willing to produce it (marginal cost). Step function

Producer Surplus Producer surplus (PS) is the area above the inverse supply curve and below the market price up to the quantity purchased by the consumer. Smooth inverse supply function

Producer’s Surplus: A Mathematical Application Suppose that the supply function is given by Q S = 2P. If the market price P = 10, what is the producer’s surplus? Given the market price P = 10, a producer’s quantity supplied Q S = 2P = 2*10 = 20 So the producer’s surplus (the area of the triangle between the price line and the inverse supply curve) is PS = ½ (20*10) = 100 If the market price falls to P = 5, how the producer’s surplus would change? Given the market price P = 5, a producer’s quantity supplied Q S = 2P = 2*5 = 10 So the producer’s surplus (the area of the triangle between the price line and the inverse supply curve) is PS = ½ (5*10) = 25 The change in producer’s surplus, ∆PS = 25 – 100 = – 75

Consumers’ Surplus in the Market

Producers’ Surplus in the Market

Social Surplus or Social Welfare Gains

Social Surplus: A Mathematical Application Suppose that the market demand function is given by Q D = 40 – 2P and the market supply is given by Q S = 2P. What is the social surplus? At the market equilibrium, Q S = Q D 2P = 40 – 2P => 4P = 40=> P = 10 At this price, equilibrium quantity exchanged is Q S = 2P = 2*10 = 20 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 10 = 10. CS = ½ (10*20) = 100 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 10 – 0 = 10. PS = ½ (10*20) = 100 The social surplus, W = CS + PS = = 200

Competition Maximizes Welfare How should we measure society’s welfare? If we agree to weighting the well-being of consumers and producers equally, then welfare can be measured W = CS + PS Producing the competitive quantity maximizes welfare. Put another way, producing less than the competitive level of output lowers total welfare. Deadweight Loss (DWL) is the name for the net reduction in welfare from the loss of surplus by one group that is not offset by a gain to another group.

How Competition Maximizes Welfare The reason that competition maximizes welfare is that price equals marginal cost at the competitive equilibrium. Consumers value the last unit of output by exactly the amount that it costs to produce it. A market failure is inefficient production or consumption, often because a prices exceeds marginal cost. Example: Deadweight loss of Christmas presents

How Competition Maximizes Welfare Reduce output below competitive level, Q 1 to Q 2, lowers social surplus by the area (C+E), which equals DWL. Producing more than the competitive level of output also lowers total welfare (by area B, which equals DWL).

Policies That Shift Demand and Supply Curves Welfare is maximized at the competitive equilibrium Government actions can move us away from that competitive equilibrium Thus, welfare analysis can help us predict the impact of various government programs We will examine several policies that shift market demand: – Change in consumers’ income – Sales tax collected from the consumers – Price subsidy We will examine several policies that shift supply: 1.Restricting the number of firms 2.Raising entry and exit costs

Policies That Shift Demand Curves Change in Consumers’ Income Income Tax or Direct Transfers from the Government Increase in income shifts the demand curve from D to D 1. Resulting in a change in the equilibrium price from P 1 to P 2 and equilibrium quantity from Q 1 to Q 2. Initial CS = abP 1 Later CS = edP 2 Not sure if CS increased or decreased. Initial PS = cbP 1 Later PS = cdP 2 Increase in PS Initial Total Surplus = abc Later Total Surplus = edc An increase in Total Surplus Society overall is better off due to an increase in consumer income. Q P D S Q1Q1 P1P1 a b c D1D1 Q2Q2 P2P2 d e

Policies That Shift Demand Curves Sales Tax Collected from the Consumers Sales Tax A new sales tax causes the price that consumers pay to rise and the price that firms receive to fall. The former results in lower CS The latter results in lower PS New tax revenue is also generated by a sales tax and, assuming the government does something useful with the tax revenue, it should be counted in our measure of welfare:

Per Unit (Specific) Sales Tax Collected from Consumers Before Sales TaxAfter Sales tax Consumers’ SurplusA + B + C + D + EA + B Producers’ SurplusF + G + H + II Tax RevenueC + D + F + G Social welfare GainA + B + C + D + E + F + G + H + IA + B + C + D + F + G + I Deadweight LossE + H

Change in Social Surplus: Sales Tax Paid by Buyers Suppose that the market demand function is given by Q D = 40 – 2P and the market supply is given by Q S = 2P. What is the social surplus? Now, suppose that the government imposes a $2 tax per unit of the commodity. The tax will be collected from the consumers. What would be the social welfare loss? Previously, we calculated that the social welfare before tax was W = 200. After tax, the consumers pay the equilibrium price plus the tax, for each unit of commodity purchased. The inverse demand function without tax is P = 20 – (1/2)Q D ; Since the consumers pay the tax, it would shift consumers’ demand to the left by the tax amount. So, the inverse demand function with tax would be P + 2 = 20 – (1/2)Q D => P = 18 – (1/2)Q D => (1/2)Q D = 18 – P => Q D = 36 – 2P

At the market equilibrium, Q S = Q D 2P = 36 – 2P => 4P = 36=> P = 9 At this price, equilibrium quantity exchanged is Q S = 2P = 2*9 = 18 The inverse demand function is P = 18 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus (P +T), that is 20 – (9+2) = 7. CS = ½ (9*18) = 81 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 9 – 0 = 9. PS = ½ (9*18) = 81 The tax revenue, T = 2*18 = 36 The new social surplus, W* = CS + PS + T= = 198 So, the loss is social welfare is, DWL = W – W* = = 2 Change in Social Surplus: Sales Tax Paid by Buyers

The Effect of a Price Subsidy to the Sellers Before Price SubsidyAfter Price Subsidy Consumers’ Surplus Producers’ Surplus Cost to Tax Payers Social welfare Gain Deadweight Loss

The Effect of a Price Subsidy to the Sellers Before Price SubsidyAfter Price Subsidy Consumers’ SurplusA + CA + C + F + G Producers’ SurplusF + HC + D + F + H Cost to Tax Payers − (C + D + E + F + G) Social welfare GainA + C + F + HA + C + F + H − E Deadweight LossE

Policies That Shift Supply Curves Entry Barriers: raising entry costs A LR barrier to entry is an explicit restriction or a cost that applies only to potential new firms (e.g. large sunk costs). Indirectly restricts the number of firms entering Costs of entry (e.g. fixed costs of building plants, buying equipment, advertising a new product) are not barriers to entry because all firms incur them. Exit Barriers: raising exit costs In SR, exit barriers keep the number of firms high In LR, exit barriers limit the number of firms entering Example: job termination laws Sales Tax Collected from the Sellers – Shifts the supply curve to the left – It causes the price that consumers pay to rise and the price that firms receive to fall.

Sales tax imposed on the sellers generates tax revenue of B+D and DWL of C+E. Policies That Shift Supply Curves Sales Tax Collected from the Sellers

Change in Social Surplus: Sales Tax Paid by Sellers Suppose that the market demand function is given by Q D = 40 – 2P and the market supply is given by Q S = 2P. What is the social surplus? Now, suppose that the government imposes a $2 tax per unit of the commodity. The tax will be collected from the consumers. What would be the social welfare loss? Previously, we calculated that the social welfare before tax was W = 200. After tax, the consumers pay the equilibrium price plus the tax, for each unit of commodity purchased. The inverse supply function without tax is P = (1/2)Q S ; Since the sellers pay the tax, it would shift the supply to the right by the tax amount. So, the inverse demand function with tax would be P – 2 = (1/2)Q S => P = 2 + (1/2)Q S => (1/2)Q S = – 2 + P => Q S = – 4 + 2P

At the market equilibrium, Q S = Q D – 4 + 2P = 40 – 2P => 4P = 44=> P = 11 At this price, equilibrium quantity exchanged is Q S = – 4 + 2P = – 4 + 2*11 = 18 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus (P), that is 20 – 11= 9. CS = ½ (9*18) = 81 The producer price received P = 11 – 2 = 9; PS = ½ (9*18) = 81 The tax revenue, T = 2*18 = 36 The new social surplus, W* = CS + PS + T= = 198 So, the loss is social welfare is, DWL = W – W* = = 2 Change in Social Surplus: Sales Tax Paid by Sellers

Important Questions About Tax Effects Does it matter whether the tax is collected from producers or consumers? Tax incidence is not sensitive to who is actually taxed. A tax collected from producers shifts the supply curve back. A tax collected from consumers shifts the demand curve back. Under either scenario, a tax-sized wedge opens up between demand and supply and the incidence analysis is identical. Does it matter whether the tax is a unit tax or an ad valorem tax? If the ad valorem tax rate is chosen to match the per unit tax divided by equilibrium price, the effects are the same.

Policies That Create a Wedge Between Supply and Demand Curves Welfare is maximized at the competitive equilibrium Government actions can move us away from that competitive equilibrium Thus, welfare analysis can help us predict the impact of various government programs We will examine several policies that create a wedge between S and D: 1.Price floor 2.Price ceiling

Price Floor A price floor, or minimum price, is the lowest price a consumer can legally pay for a good. Example: agricultural products Minimum price is guaranteed by government, but is only binding if it is above the competitive equilibrium price. Deadweight loss generated by a price floor reflects two distortions in the market: 1.Excess production: More output is produced than consumed 2.Inefficiency in consumption: Consumers willing to pay more for last unit bought than it cost to produce Policies That Create a Wedge Between Supply and Demand Curves

Price floor creates wedge that generates excess production of Q s – Q d and DWL of C+F+G. Policies That Create a Wedge Between Supply and Demand Curves

Price Ceiling A price ceiling, or maximum price, is the highest price a firm can legally charge. Example: rent controlled apartments Maximum price is only binding if it is below the competitive equilibrium price. Deadweight loss may underestimate true loss for two reasons: 1.Consumers spend additional time searching and this extra search is wasteful and often unsuccessful. 2.Consumers who are lucky enough to buy may not be the consumers who value it the most (allocative cost). Policies That Create a Wedge Between Supply and Demand Curves

Price ceiling creates wedge that generates excess demand of Q d – Q s and DWL of C+E. Policies That Create a Wedge Between Supply and Demand Curves

International Trade Policies Finally, we use welfare analysis to examine government policies that are used to control international trade: 1.Free trade 2.Ban on imports (no trade) 3.Set a tariff 4.Set a quota Welfare under free trade serves as the baseline for comparison to effects of no trade, quotas and tariffs. Assume zero transportation costs and horizontal supply curve for the potentially imported good Assumptions imply U.S. can import as much as it wants at p * per unit.

Free Trade vs. No Trade With free trade, domestic producers supply Q=8.2 and imports of Q=4.9 fill out our additional demand for oil at the low world price. With no trade, we lose surplus equal to area C. This is the DWL of a total ban on trade.

Social Surplus: No Trade (Autarky) Suppose that the market demand function is given by Q D = 40 – 2P and the market supply is given by Q S = 2P. What is the social surplus? At the market equilibrium, Q S = Q D 2P = 40 – 2P => 4P = 40=> P = 10 At this price, equilibrium quantity exchanged is Q S = 2P = 2*10 = 20 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 10 = 10. CS = ½ (10*20) = 100 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 10 – 0 = 10. PS = ½ (10*20) = 100 The social surplus, W = CS + PS = = 200

Social Surplus: Free Trade Suppose that the country adopts a free trade policy. So, the country can import the good from other countries at the World price. Suppose that world price of the good is P w = 5 The country’s domestic market demand and supply remain the same as before; Q D = 40 – 2P and Q S = 2P But, under free trade, the domestic price would be equal to the world price. At this new lower price consumers would purchase more, but producers would sell less. Q D = 40 – 2P w => Q D = 40 – 2*5=> Q D = 30 Q S = 2P => Q S = 2*5 => Q S = 10 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 5 = 15. CS = ½ (15*30) = 225 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 5 – 0 = 5. PS = ½ (5*10) = 25 The social surplus, W = CS + PS = = 250

Tariffs A tariff is essentially a tax on imports and there are two common types: Specific tariff is a per unit tax Ad valorem tariff is a percent of the sales price Assuming the U.S. government institutes a tariff on foreign crude oil: 1.Tariffs protect American producers of crude oil from foreign competition. 2.Tariffs also distort American consumers’ consumption by inflating the price of crude oil.

Tariffs A $5 per unit (specific) tariff raises the world price, which increases the quantity supplied domestically and decreases the quantity imported. Tariff revenue of area D is generated by the U.S. DWL is equal to C+E.

Social Surplus: Trade with Tariff Now suppose that the government of the importing country imposes a 20% ad valorem tariff on imports. So, the price in the country would be P t = P w + 0.2* P w = *5 = 6 The country’s domestic market demand and supply still remain the same as before Q D = 40 – 2P and Q S = 2P At this new price consumers would purchase less than the free-trade quantity, but domestic producers would sell more than the free-trade quantity. Q D = 40 – 2P t => Q D = 40 – 2*6=> Q D = 28 Q S = 2P => Q S = 2*6 => Q S = 12 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 6 = 14. CS = ½ (14*28) = 196 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 6 – 0 = 5. PS = ½ (6*12) = 36 The government’s tariff revenue T = 1*(28-12) = 16 The social surplus, W = CS + PS + T= = 248 Dead-weight loss from tariff = = 2

Quotas A quota is a restriction on the amount of a good that can be imported. When analyzed graphically, a quota looks very similar to a tariff. A tariff is a restriction on price A quota is a restriction on quantity One can find a tariff and a quota that generate the same equilibrium The only difference is that quotas do not generate any additional revenue for the domestic government.

Quotas An import quota of 2.8 millions of barrels of oil per day increases the quantity supplied domestically and decreases the quantity imported. Equivalent to $5 per unit tariff DWL is equal to C+D+E because no tariff revenue is generated.

Social Surplus: Trade with Quota Now suppose that the government of the importing country imposes an import quota of 16 units of the commodity, but no tariff at all. This would also result into a domestic price P Q = 6, as domestic producers would supply 12 units at this price, Q S = 12. The consumers would purchase 28 units, Q D = 28 The inverse demand function is P = 20 – (1/2)Q D ; the height of the triangle is the intercept of the inverse demand curve minus P, that is 20 – 6 = 14. CS = ½ (14*28) = 196 The inverse supply function is P = (1/2)Q S ; the height of the triangle is P minus the intercept of the inverse supply curve, that is 6 – 0 = 5. PS = ½ (6*12) = 36 The government’s tariff revenue T = 0 The social surplus, W = CS + PS + T= = 232 Dead-weight loss from quota = = 18

Difficulty in Measuring Consumer’s Surplus Alternative Measures How much are consumers helped or harmed by shocks that affect the equilibrium price and quantity? Shocks may come from new inventions that reduce firm costs, natural disasters, or government-imposed taxes, subsidies, or quotas. You might think utility is a natural measure of consumer welfare. Utility is problematic because: we rarely know a consumer’s utility function Estimating consumer demand is not an easy task utility doesn’t allow for easy comparisons across consumers A better measure of consumer welfare is in terms of dollars.

Alternative Measures: Compensating Variation and Equivalent Variation Two Alternative Measures: Compensating variation is the amount of money we would have to give a consumer after a price increase to keep the consumer on their original indifference curve. Equivalent variation is the amount of money we would have to take away from a consumer to harm the consumer as much as the price increase did.

Compensating Variation and Equivalent Variation Indifference curves can be used to determine compensating variation (CV) and equivalent variation (EV).

Three Measures: CS, CV, and EV Relationship between these measures for normal goods: |CV| > |∆CS| > |EV| For small changes in price, all three measures are very similar for most goods.

Effects of Government Policies on Consumer Welfare Government programs can alter consumers’ budget constraints and thereby affect consumer welfare. Examples Quota: reduces the number of units that a consumer buys Subsidy: causes a rotation or parallel shift of the budget constraint Welfare programs: may produce kinks in budget constraint

Effects of Government Policies: Quotas Quotas limit how much of a good consumers can purchase. Quota of 12 units generates kink in budget line and removes shaded triangle region from individual’s choice set. Because of this quota, the consumer’s equilibrium will be at the kink of the budget line, that is tangent to a lower indifference curve indicating lower level of utility.

Effects of Government Policies: Welfare Programs Welfare programs provide either in-kind transfers or a comparable amount of cash to low-income individuals. Example: food stamps $100 in food stamps (in- kind) generates kinked budget line. $100 cash transfer increases opportunity set further.

Effects of Government Policies: Welfare Programs Because food stamps can only be used on food, consumers are potentially worse off if they would find it optimal to consume less food and more other goods than allowed by the program. Despite this, food stamps are used rather than comparable cash transfers in order to: reduce expenditures on drugs and alcohol encourage appropriate expenditure on food from a nutrition standpoint maintain program support from taxpayers, who feel more comfortable providing in-kind rather than cash benefits

Effects of Government Policies: Subsidies Subsidies either lower prices or provide lump-sum payments to low-income individuals. Example: child care subsidy Reducing price of child care rotates budget line out Unrestricted lump-sum payment (equal to taxpayers’ cost of the subsidy) shifts budget line out in a parallel fashion and increases opportunity set