problem 1: The annual demand curve for the perfectly competitive milk market is P = 9 - 0.01 Q. This market is in long run equilibrium. The price of milk is $2.00 and each of the producers operate at minimum long run average cost (LAC).
The LAC function for each individual identical farm can be represented by the equation where q is millions of gallons/year.
LAC = 3.00 -q + 0.25 q^{2}
a) How many gallons of milk are sold per year?
b) What is the dollar value of consumer surplus?
c) Assume that a new technology causes the LAC function for dairy farming to change to:
LAC = 2.7 - 1.2 q + 0.3 q^{2}
d) In the new long run equilibrium, how will the nu mber of farms change?
e) In the new long run equilibrium, how will the production of each farm change?
f) In the new long run equilibrium, how will the expenditure on milk change?
g) Ignore the technology change and demand function change stated above. Assume that a monopolist buys all of the dairy farms. The monopolist has LAC = LMC which coincides with the long run supply curve (LS = $2) under perfect competition. What is the profit-maximizing price-quantity combination?
h) What is the dollar value of the deadweight loss from monopoly?
problem 2: A monopolist, say a cable television franchise has two distinct markets: residences and businesses. Suppose that the respective demand functions for basic services are:
Residences: P = 55 - 0.0071428 Q
Businesses: P = 130 -0.1 Q
Where P is the price per month and Q is subscribers per month. The marginal and average cost of providing service is $5 per month per subscriber.
a) First, if the monopolist combines the two markets and charges the same price to all customers to maximize profit, what will the price and quantity be?
b) Suppose all firms in an industry have the following long-run total cost curve: c(y) = 0:5y^{2} + 20y. Derive the average cost curve and marginal cost curve of a firm. Sketch both curves in a figure.
problem 3: You are the chief economist of the County Regulatory Commission. The local cable TV monopoly franchise is regulated. The consulting firm provides the long run total cost and demand function estimates for the franchise:
LTC = Q^{3} – 8Q^{2} + 50Q and P = 140 - 50Q
Where Q represents thousands of monthly subscribers and P is monthly price.
a) If the franchise were not regulated what price-quantity combination would maximize profit?
b) Now find the price-quantity combination if a regulatory policy of average cost pricing is imposed.
c) Given your answers to a and b, find out the change in consumers’ surplus.
problem 4: Assume that we know that the domestic supply function for peanuts in the US is:
P = 4 + 0.001Q
where Q is the number of bushels per year and P is the price in dollars per bushel.
Suppose that we know that the domestic demand function for peanuts (holding domestic income and other demand shifting variables constant) is:
P = 30 - 0.004 Q.
a) If there is no international trade, what is the equilibrium price and quantity?
b) Suppose that the world price of peanuts is $5 per bushel and international trade is not restricted. Find the domestic production and consumption of peanuts and US imports at the world price.
c) Suppose that the US government wishes to restrict imports to 1000 (million bushels) per year. What $/bushel tariff would have this effect?
d) How much tariff revenue per year would a $1/bushel tariff on peanuts generate?
problem 5: A monopolist faces the demand and total cost functions below. To maximize profit, the monopolist chooses the optimal level of output per month (Q), price (P) and advertzing expenditure per month (A). Find the optimal value of A.
P = 235 - 0.02 Q + 0.1A^{1/2} TC = 25Q + A
Firm’s production function is Q = 5L^{2/3}K^{1/3}. find out the marginal products of K and L. Does this production function exhibit constant, increasing, or decreasing returns to scale? What is the marginal rate of technical substitution of L for K for this production function?
problem 6: The market structure of home video gaming systems is best characterized by monopolistic competition. Quasar Entertainment is one of the producers in this market. The inverse demand for Quasar systems is:
P = 500 - 9.75Q
Quasar's cost function is: C(Q) = 0.25Q^{2} + 6. Determine Quasar's profit maximizing level of output and the price charged to customers. Is the market in a long-run equilibrium?