Econ 255: Test Two

Jane pays Chuck $50 to mow her lawn every week. When the government levies a mowing tax of $10 on Chuck, he raises his price to $60. Jane continues to hire him at the higher price. What is the change in producer surplus, change in consumer surplus, and deadweight loss?

$0, -$10, $0

The government places a tax on the purchase of socks. (a) Illustrate the effect of this tax on equilibrium price and quantity in the socks market. Identify the following areas both before and after the imposition of the tax: total spending by consumers, total revenue for producers, and government tax revenue. (b) Does the price received by producers rise or fall? Can you tell whether total receipts for producers rise or fall? Explain. (c) Does the price paid by consumers rise or fall? Can you tell whether total spending by consumers rises or falls? Explain carefully. If total consumer spending falls, does consumer surplus rise? Explain.

(a) Figure 6 illustrates the market for socks and the effects of the tax. Without a tax, the equilibrium quantity would be Q1, the equilibrium price would be P1 x Q1, which equals area B+C+D+E+F, and government revenue is zero. The imposition of a tax places a wedge between the price buyers pay, Pb, and the price sellers receive, Ps, where Pb=Ps + tax. The quantity sold declines to Q2. Now total spending by consumers is Pb x Q2, which equals area A+B+C+D, total revenue for producers is Ps x Q2, which is area C+D, and government tax revenue is Q2 x tax, which os area A+B. (b) Unless supply is perfectly elastic or demand is perfectly inelastic, the price received by producers falls because of the tax. Total receipts for producers fall, because producers lose revenue equal to area B+E+F. (c) The price paid by consumers rises, unless demand is perfectly elastic or supply is perfectly inelastic. Whether total spending by consumers rises or falls depends on the price elasticity of demand. If demand is elastic, the percentage decline in quantity exceeds the percentage increase in price, so total spending declines. If demand is inelastic, the percentage decline in quantity is less than the percentage increase in price, so total spending rises. Whether total consumer spending falls or rises, consumer surplus declines because of the increase in price and reduction in quantity.

Consider a market in which Bert from problem 4 is the buyer and Ernie from problem 5 is the seller. (a) Use Ernie's supply schedule and Bert's demand schedule to find the quantity supplied and quantity demanded at prices of,, and ,, and . Which of these prices brings supply and demand into equilibrium? (b) What are consumer surplus, producer surplus, and total surplus in this equilibrium? (c) If Ernie produced and Bert consumed one fewer bottle of water, what would happen to total surplus? (d) If Ernie produced and Bert consumed one additional bottle of water, what would happen to total surplus?

(a) Price $2; $4; $6 Quantity Supplied 1; 2; 3 Quantity Demanded 3; 2; 1 -Only a price of $4 brings supply and demand into equilibrium, with and equilibrium quantity of two. (b) At a price of $4, consumer surplus is $4 and producer surplus is $4, as shown in Problems 3 and 4 above. The total surplus is $4+$4=$8. (c) If Ernie produced one less bottle, his producer surplus would decline to $3, as shown in problem 4 above. If Bert consumed one less bottle, his consumer surplus would decline to $3, as shown in problem 3 above. So total surplus would decline to $3+$3=$6. (d) If Ernie produced one additional bottle of water, his cost would be $5, but the price is only $4, so his producer surplus would decline by $1. If Bert consumed one additional bottle of water, his value would be $3, but the price is $4, so his consumer surplus would decline by $1. So total surplus declines by $1+$1=$2.

Suppose that a market is described by the following supply and demand equations: (a)Solve for the equilibrium price and the equilibrium quantity. (b) Suppose that a tax of is placed on buyers, so the new demand equation is Qd=300-(P+T) Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? (c) Tax revenue is TxQ. Use your answer to part (b) to solve for tax revenue as a function of . Graph this relationship for T between 0and 300 . (d) The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is ½ x base x height, solve for deadweight loss as a function of . Graph this relationship for T between 0 and 300. (Hint: Looking sideways, the base of the deadweight loss triangle is T , and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.) (e) The government now levies a tax on this good of $200 per unit. Is this a good policy? Why or why not? Can you propose a better policy?

(a) Setting quantity supplied equal to quantity demanded gives 2P = 300 - P. Adding P to both sides of the equation gives 3P = 300. Dividing both sides by 3 gives P = 100. Substituting P = 100 back into either equation for quantity demanded or supplied gives Q = 200. (b) Now P is the price received by sellers and P +T is the price paid by buyers. Equating quantity demanded to quantity supplied gives 2P = 300 − (P+T). Adding P to both sides of the equation gives 3P = 300 - T. Dividing both sides by 3 gives P = 100 -T/3. This is the price received by sellers. The buyers pay a price equal to the price received by sellers plus the tax (P +T = 100 + 2T/3). The quantity sold is now Q = 2P = 200 - 2T/3. (c) Because tax revenue is equal to T x Q and Q = 200 - 2T/3, tax revenue equals 200T − 2T2/3. Figure 10 (on the next page) shows a graph of this relationship. Tax revenue is zero at T = 0 and at T = 300. (d) As Figure 11 shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 × base × height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity (2T/3). So the deadweight loss equals 1/2 × T × 2T/3 = T2/3. This rises exponentially from 0 (when T = 0) to 30,000 when T = 300, as shown in Figure 12. (e) A tax of $200 per unit is a bad policy, because tax revenue is declining at that tax level. The government could reduce the tax to $150 per unit, get more tax revenue ($15,000 when the tax is $150 versus $13,333 when the tax is $200), and reduce the deadweight loss (7,500 when the tax is $150 compared to 13,333 when the tax is $200).

One of the largest changes in the economy over the past several decades is that technological advances have reduced the cost of making computers. (a) Draw a supply-and-demand diagram to show what happened to price, quantity, consumer surplus, and producer surplus in the market for computer. (b) Forty years ago, students used typewriters to prepare papers for their classes; today they use computers. Does that make computers and typewriters complements or substitutes? Use a supply-and-demand diagram to show what happened to price, quantity, consumer surplus, and producer surplus in the market for typewriters. Should typewriter producers have been happy or sad about technological advance in computers? (c) Are computers and software complements or substitutes? Draw a supply-and-demand diagram to show what happened to price, quantity, consumer surplus, and producer surplus in the market for software. Should software producers have been happy and sad about the technological advance in computers? (d) Does this analysis help explain why software producer Bill Gates is one of the world's richest men?

(a) The effect of falling production costs in the market for computers resulted in a shift to the right in the supply curve, as shown in Figure 14. As a result, the equilibrium price of computers declined and the equilibrium quantity increased. The decline in the price of computers increased consumer surplus from area A to A+B+C+D, an increase in the amount B+C+D. {Figure 14 and 15: Prior to the shift in supply, producer surplus was areas B+E (the area above the supply curve and below the price). After the shift in supply, producer surplus is areas E+F+G. So producer surplus changes by the amount F+G-B, which may be positive or negative. The increase in quantity increases producer surplus, while the decline in the price reduces producer surplus. Because consumer surplus rises by B+C+D and producer surplus rises by F+G-B, total surplus rises by C+D+F+G.} (b) Typewriters and computers are substitutes. The decline in the price of computers means that people substituted computers for typewriters, shifting the demand for typewriters to the left, as shown in figure 15. The result is a decline in both the equilibrium price and equilibrium quantity of typewriters. Consumer surplus in the typewriter market changes from area A+B to A+C, a net change of C-B. Producer surplus changes from area C+D+E to area E, a net loss of C+D. Typewriter producer are sad about technological advances in computers because their producer surplus declines. (c) Software and computers are computers are complements. When the price of computers decreases, the demand for software increases. The demand for software shifts to the right, as shown in figure 16. The result is an increase in both the price and quantity of software. Consumer surplus in the software market changes from B+C to A+B, a net change of A-C. Producer surplus changes from E to C+D+E, an increase of C+D, so software producers should be happy about the technological progress in computers. (d) Yes, this analysis helps explain why Bill Gates is one the world's richest people. His company producers a lot of software and the producer surplus in the software market increased with the technological advance in computers.

A friend of yours is considering two cell phone service providers. Provider A charges $120 per month for the service regardless of the number of phone calls made. Provider B does not have a fixed service fee but instead charges $1 per minute for calls. Your friend's monthly demand for minutes of calling is given by the equation Q D=150 - 50 P, where P is the price of a minute. (a) With each provider, what is the cost to your friend of an extra minute on the phone? (b) In the light of your answer to (a), how many minutes with each provider would your friend talk on the phone? (c) How much would she end up paying each provider every month? (d) How much consumer surplus would she obtain with each provider? (e) Which provider would you recommend that your friend choose? Why?

(a) With Provider A, the cost of an extra minute is $0. With Provider B, the cost of an extra minute is $1. (b) With Provider A, my friend will purchase 150 minutes [=150 - (50)(0)]. With Provider B, my friend would purchase 100 minutes [=150-(50)(1)]. (c) With Provider A, she would pay $120. With Provider B, he would pay $100. (d) Figure 17 shows the friend's demand. With Provider A, she buys 150 minutes and her consumer surplus is equal to (1/2)(2)(100)=100. (e) I would recommend Provider A because she receives greater consumer surplus when buying from that provider.

There are four consumers willing to pay the following amount for haircuts: Gloria: Jay: Claire: Phil: There are four haircutting businesses with the following costs: Firm A: Firm B: Firm C: Firm D: Each firm has the capacity to produce only one haircut. For efficiency, how many haircuts should be given? Which businesses should cut hair and which consumers should have their hair cut? How long is the maximum possible total surplus?

Figure 13 shows supply and demand curves for haircuts. Supply equals demand at a quantity of three haircuts and a price between $4 and $5. Firms A, C, and D should cut the hair of Claire, Gloria, and Phil. Jay's willingness to pay is to low and a firm B's cost are to high, so they do not participate. The maximum total surplus is the area between the demand and supply curves, which totals $11 ($8 value minus $2 cost for the first haircut, plus $7 value minus $3 cost for the second, plus $5 value minus $4 cost for third).

This chapter analyzed the welfare effects of a tax on a good. Consider now the opposite policy. Suppose that the government subsidizes a good: For each unit of the good sold, the government pays to the buyer. How does the subsidy affect consumer surplus, producer surplus, tax revenue, and total surplus? Does a subsidy lead to a deadweight loss? Explain.

Figure 7 illustrates the effects of the $2 subsidy on a good. Without the subsidy, the equilibrium price is P1 and the equilibrium quantity is Q1. With the subsidy, buyers pay price PB, producers receive price PS (where PS = PB + $2), and the quantity sold is Q2. The following table illustrates the effect of the subsidy on consumer surplus, producer surplus, government revenue, and total surplus. Because total surplus declines by area D + H, the subsidy leads to a deadweight loss in that amount.

Producing a quantity larger than the equilibrium of supply and demand is inefficient because the marginal buyer's willingness to pay is

positive but less than the marginal seller's cost.

Jen values her time at $60 and hour. She spends 2 hours giving Colleen a massage. Colleen was willing to pay as much as $300 for the massage, but they negotiate a price of $200. In this transaction,

consumer surplus is $20 larger than producer surplus.

The Laffer curve illustrates that, in some circumstances, the government can reduce a tax on a good and increase the

government's tax revenue.

When a market is in equilibrium, the buyers are those with the ________ willingness to pay and sellers are those with the ______ cost.

highest, lowest

Peanut butter has an upward-sloping supply curve and a downward-sloping demand curve. If a 10 cent per pound tax is increased to 15 cents, the government's tax revenue

increases by less than 50 percent and may even decline.

If a policymaker wants to raise revenue by taxing goods while minimizing the deadweight losses, he should look for goods with ____ elasticities of demand and _____ elasticities of supply.

small, small