Question

Suppose a perfectly competitive firm has marginal and total costs given by M C = 3 + 2q and T C = 2 + 3q + q2, respectively, where q is the quantity of output produced by the firm. In a monetary union the firm faces a constant price p1 = 9 for its product. Outside of the monetary union with a flexible exchange rate it faces a 50-50 chance of p2 = 11 or p3 = 7. The firm decides on the profit maximizing quantity q by setting p = MC which maximizes its profit π = (p ∗ q) − TC.

(a) What are the firm’s profit maximizing quantity, price and profit in a monetary union?

(b) What is the average profit with a flexible exchange rate?

(c) Does more exchange rate certainty in a monetary union lead to higher profits for the firm?

Answer 1

Answer:-

Let us solve the above problem with the help of equilibrium conditions of a perfectly competitive market as follows:

We know that at perfect condition the equilibrium condition is

MR = MC = P

Given the price in the monetary union p1 = 9 and the MC, therefore at equilibrium we have

MC = P

3 + 2q = 9

or, q = 3. This is the profit maximizing quantity.

Now the profit is

or profit = 27 - 20 = 7

Hence the firm's profit maximizing quantity, price and profit in a monetary union are q = 3, p = 9, profit = 7.

(b) Since there is a 50-50 chance that the prices will be wither 11 or 7, then the average profit will be

or,

or,

Note: since there is a 50-50 chance in opting the flexible exchange rate, so 1/2 is multiplied to the profits earned with prices p = 11 or p = 7.

Hence wth the flexible exchange rate the average profit will be 6.

(c) To answer this question we shall compare the profits of the firm in both monetary union and flexible exchange rate.

In monetary unoin the firm's profit is 7, whereas with flexible exchange rate the posibility of earning an average profit goes down to 6 as derived in question b.

Hence we can conclude that with more exchnage rate certainty in a moneytary union a firm earns higher profit.