# Problem Set 4: Market Interventions &amp; Monopoly Pricing 1. ...

## Transcribed Text

Problem Set 4: Market Interventions & Monopoly Pricing 1. Consider a small open economy. The domestic market demand function for corn is Qd = 10 - 0.5P and the domestic market supply function is Q* = P - 2, both mea- sured in billions of bushels per year. Suppose the import supply curve is infinitely elastic at a price of \$4 per bushel. (a) What are the equilibrium price and quantity? What is the domestic consumer surplus? domestic producer surplus? Show all of these numerically and graph- ically. (b) Suppose the government imposes a tariff of \$2 per bushel. What will the new equilibrium price and quantity be? What is the domestic consumer surplus? domestic producer surplus? government tax revenue? dead weight loss? Show all of these numerically and graphically. (c) Ignore part (b). Suppose the government impose an import quota such that the domestic equilibrium price is PA = 6. What is the domestic consumer surplus? domestic producer surplus? Foreign producer surplus? dead weight loss? Show all of these numerically and graphically. 2. A monopolist operates with the following data on cost and demand. It has a total fixed cost of \$1, .000 and a total variable cost of Q2, where Q is the number of units of output it produces. The firm's demand function is Qd = 60 - 0.5P. The firm expects the conditions of demand and cost to continue in the foreseeable future. (a) What is the inverse market demand curve? (b) What is the marginal revenue function that corresponds to this demand curve? (c) What is the monopolist's marginal cost function? (d) What is the firm's revenue if it operates and it maximizes profit? (e) What is the dead weight loss from the monopoly pricing? (f) Should the firm continue to operate in the short run, or should it shut down? Explain.

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1. Considering a small open economy with demand
Qd= 10-0.5P and Qs= P-2
We have the equilibrium quantity and price at
10-0.5P= P-2
10+2 =P+0.5P
12=1.5P
P= 8
Q= 10-4=6

a) When there are imports from outside, at \$4 per bushel, the world price is at \$4 which is shown in the following figure.
When the world price is at \$4, Qd= 10-0.5(4) = 10-2 = 8
Qs= P-2 = 4-2 = 2
The imported quantity is at 8-2 = 6 units...

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