Question

Your firm is a monopoly supplier of a good. The inverse demand for your good (in dollars) is given by P=250−0.02Q . Your firm's cost function (in dollars) is C(Q)=400000+22Q+0.01Q2. Some of that cost comes from a critical part that you import from England that currently costs you $12.00 US for every unit of output that you produce.

The current exchange rate is 1.20 $/£. How much profit (in $US) does your firm make? Round your answer to the nearest penny.

If the exchange rate rises to 1.50 $/£, how much profit (in $US) does your firm make? Round your answer to the nearest penny.

Answer 1

If firm produces Q quantity Revenue = (250-0.02Q)*Q = 250Q - 0.02Q²

Hence Profit = 250Q - 0.02Q² - (400000+22Q+0.01Q²)

or, Profit = 250Q - 0.02Q² - 400000-22Q-0.01Q²

or, Profit, P = -400000+228Q -0.03Q²

At Maximum Profit , dP/dQ = 0

hence, dP/dQ = 0 = d/dQ( -400000+228Q -0.03Q²)

or, 0 = 0+228-0.03*2Q

or, 0.06Q =228

or, Q = 228/0.06 = 3800

Hence Profit maximizing quantity is 3800 units

Profit at Q=3800 = -400000+228*3800 -0.03*3800²

or, P = -400000+866400-433200 = $33200

Total Cost of critical part for 3800 units = 12*3800 = $45600

Total Cost of critical part for 3800 units at new exchange rate= 45600*1.5/1.2 =$57000

Hence Total Cost increases by 57000-45600 = $11400

Hence Net Profit will reduce to 33200-11400 = $21800