Perfectly Competitive Markets: Short Run and Long Run Equilibria

The perfectly competitive firm and market in the short run.In Venice, there are fifty souvenir stores that sell plastic replicas of the local gondola boats. Each store has a short run total cost function TCSR(q) = 0.1q2 + 2q + 200. In the short-run, 80% of the fixed cost is sunk. The demand for plastic gondolas is QD = 3,000 – 100P.

a) What is the FC, the VC, the MC and the AVC of the typical souvenir store in Venice?

b) In a graph, measuring quantity along the horizontal axis draw the MC, AVC and AC curves.

c) What do economists mean by “shut down price”? Assuming that in the short run the fixed cost is sunk, what is the shut down price in the Venice market for plastic gondolas?

d) Find the supply function of the typical souvenir store. Keep in mind that at prices below the shut down price quantity supplies is zero.

e) Sum across firms and find the market supply for plastic gondolas in Venice.

f) Find the equilibrium price and the equilibrium quantity of plastic gondolas.

g) In a diagram, measuring the market quantity of plastic gondolas along the horizontal axis and the price of a plastic gondola along the vertical axis, draw the market demand and the market supply and clearly indicate the market equilibrium.

h) What do economists mean by “consumer surplus”?

Would you say that in this market the change in consumer surplus is a good measure of the welfare gains or losses a policy would impose on consumers? Briefly discuss. Stitching: Review your notes on the Supply and Demand model. In particular, remind yourself of the comparative statics formulas you learned in the first week of classes.

i) Keeping those in mind, how would a $1 per plastic gondola tax collected from souvenir stores impact the equilibrium price of gondolas?

j) How much revenue would the tax collect for the City of Venice?

k) How would the tax impact a souvenir store’s profit from selling plastic gondolas?

l) If you were a souvenir store-owner, would you rather include the $1 tax in the price and post the post-tax price on each plastic gondola or post the pre-tax price on the gondolas and hang a sign on the wall stating “ The City of Venice collects a $1 “Save Venice” contribution on every plastic gondola sold in this store. The contribution will be added at the counter.” Briefly discuss.

Problem 2

The perfectly competitive firm and market in the short run Consider a perfectly competitive market where one hundred firms compete for customers. The typical firm has a technology summarized in the total cost function TC(q) = 100+ q + 0.05q2.

a) Find the short run supply function of a typical firm. Then, summing across firms find the market supply function (clearly indicate the shut down price.) On the demand side, there are one thousand potential buyers each with a daily budget of $200 and tastes represented by the quasi-linear utility U(q,M) = 9q - 0.5q2 + M where M is money left for other purchases.

b) Keeping in mind that M is a numeraire and that PM = $1, find the demand function of the typical buyer. Then, summing across buyers find the market demand.

c) In a graph, measuring quantity along the horizontal axis and price along the vertical axis draw the demand and supply curves and illustrate the equilibrium price and the equilibrium quantity.

d) Use algebra to find the equilibrium price and the equilibrium quantity. Suppose the government introduces a fill-in-the- gap price floor of $6 (i.e. a deficiency payment). The price floor guarantees the typical firm a unit revenue of $6. d) After the introduction of the price floor (deficiency payment), what is equilibrium quantity? What is equilibrium price?

e) Use the concepts of consumer surplus and producer surplus to evaluate who gains and who looses from the introduction of the fill-in-thegap price floor. f) Does the price floor increase or reduce the market efficiency? How would you evaluate the program’s impact on efficiency?

The perfectly competitive firm and market in the short run Consider a perfectly competitive market where demand is QD = 2,000 - 40P and quantity is measured in units while price is measured in dollars per unit. The long run supply is QS = 100P - 800.

a) Find the equilibrium price and the equilibrium quantity.

b) When the market is in equilibrium, what is the total expenditure in this market?

c) When the market is in equilibrium, what is the consumer surplus? What is the producer surplus? Intermediate Microeconomics Fall 2019 Prof. Musatti Problem Set 7 2

d) Suppose the government introduces a quota that restricts quantity at Q = 800. How much in total consumer and producer surplus would be lost?

e) In a graph, measuring quantity in units along the horizontal axis and price in dollars per unit along the vertical axis illustrate your finding from part d).

Problem 3

f) Does the loss in consumer and producer surplus depends on whether the price settles at P =30, at P’ = 16, or any price in between? Discuss.

g) Call P the market price after the introduction of the quota and compute consumer surplus and producer surplus as a function of P. Using algebra, show that while CS and PS depend on P their sum does not.

The perfectly competitive firm and market in the long run Consider a perfectly competitive market where the typical firm has a long run total cost of CLR(q) = 0.1q2 + 2q + 160 where in the long run the recurring fixed cost is not sunk. a) Find the long run equilibrium price.

a.1) Find the minimum efficient scale of the typical firm.

a.2) Find the typical firm’s average cost when it operates at minimum efficient scale.

a.3) In the long run, what price will prevail in this market? In words, clearly justify your answer. Suppose demand is QD = 3,200 – 100P.

b) Explain why you expect the number of firms in this market to be fifty-five. Suppose that the short run cost of the typical firm is equal to the long run cost. In the short run, however, the recurring fixed cost is sunk.

c) Find the short run supply function of the typical firm. d) Summing across firms, find the short run market supply function.

e) In a graph, measuring market demand along the horizontal axis and price along the vertical axis draw the short run demand and supply curves and the market equilibrium.

f) In a second graph, measuring the typical firm’s quantity along the horizontal axis and price along the vertical axis draw the typical firm’s AC, and MC and illustrate the long run equilibrium of the typical firm.

g) In the graphs, illustrate how a $7.5 per unit tax collected from each firm would shift the short run supply curve and change the short run equilibrium.

h) In words, explain how the tax affects firms’ short run profit and describe how the market adjusts to a new long run equilibrium.

i) Then, keeping in mind that the long run supply curve is infinitely elastic, discuss how the economic incidence of the tax evolves through time.

The perfectly competitive firm and market in the long run This question continues from the previous one. Suppose the government imposes a licensing fee of $200 per period. The fee raises the fixed cost of the typical firm from $160 to $360.

a) What is the impact of the licensing fee on the typical firm’s minimum efficient scale? Explain.

b) What is the impact of the licensing fee on the long run equilibrium price in this market? Explain.

c) Does the introduction of the licensing fee affect the number of firms in the industry? Explain.

d) What is the revenue that the government raises with the introduction of the licensing fee?

e) What is the impact of the licensing fee on buyers’ consumer surplus? Suppose that instead of the licensing fee the government decides to impose a $4 per unit tax.

f) In the long run, what is the impact of this tax on the market price?

g) How does the tax affect the long run equilibrium quantity in this market?

h) Are the licensing fee and the per unit tax equivalent policies? Do they raise the same revenue? Do they impact the market in the same way? Discuss.