Question

Your US based company exports drendels to the rest of the world. The world market for drendles is highly competitive (so competitive that changes in production in the US do not impact the world price). The current price of a drendle is €100/drendle. Company's cost fix is C(q) =50,000+50q+0.02q² in US dollars. If the exchange rate is $1.20/€ how much profit in US dollars does your firm make?

Answer 1

Price (P) must equal to marginal cost (MC) for establishing the profit-maximizing stage.

Given the total cost function is as below:

C = 50,000 + 50q + 0.02q^2 +

MC = Derivative of C with respect to q

       = 0 + {50q^(1 – 1)} + {(0.02 × 2)q^(2 – 1)}

       = 0 + 50q^0 + 0.04q

       = 50 + 0.04q

Now, price in US dollar; P = 100 × 1.20 = $120

Now, by the formula as below

P = MC

120 = 50 + 0.04q

120 – 50 = 0.04q

0.04q = 70

q = 70/0.04 = 1,750

This is the profit-maximizing quantity of the company. This is to be placed to C in order to get the value of total cost (TC).

C = 50,000 + 50q + 0.02q^2 +

    = 50,000 + 50 × 1,750 + 0.02 × 1,750^2

    = 50,000 + 87,500 + 61,250

    = 198,750

Now, for the calculation of total revenue (TR) as below:

TR = P × q

      = 120 × 1,750

      = 210,000

Now, by the formula of profit as below:

Profit = TR – C

          = 210,000 – 198,750

          = $11,250 (Answer)