Suppose you are a monopolist who faces a domestic demand curve given by Q = 1,000 –3P. Your domestic cost of production involves domestic costs per unit of 300 and a foreign cost per unit produced of 150. If the real exchange rate is 1.1, what would be the price you would charge and the quantity you would sell? How do these variables change when the real exchange rate increases by 10%?

399.17 ; 407.42

Explanation:

Given ;

Domestic cost per unit = 300

Foreign cost per unit = 150

Real exchange rate = 1.1

As a monopolist, aim is to maximize income:

Q = 1000 - 3P

THEREFORE,

Price (P) × quantity(Q) - domestic - foreign × exchange rate

P × Q - 300Q - 150Q × 1.1

P × Q - 300(1000-3P) - 150(1000-3P)×1.1

P× (1000-3P) - (300+(150×1.1))(1000-3P)

P× (1000-3P) - (465)(1000-3P)

(P-465) × (1000-3P)

1000P - 3P^2 - 465000 + 1395P

-3P^2 + 2395P-465000

P = 399.17

If real exchange rate increases by 10%,

10% of 1.1 = 0.1 × 1.1 = 0.11

0.11 + 1.1 = 1.21

simply change 1.1 to 1.21 in above equation

P× (1000-3P) - (300+(150×1.21))(1000-3P)

P× (1000-3P) - (481.5)(1000-3P)

(P-481.5) × (1000-3P)

1000P - 3P^2 - 481500 + 1444.5P

-3P^2 + 2444.5P-481500

P = 407.42

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