Consider the Home country with the demand curve for apples given by P = 20 – 2Q.

Question

Consider the Home country with the demand curve for apples given by
P = 20 – 2Q.
There is only one firm that produces apples at the marginal cost of $4 per kilo.

Assume that Home has started trading with the Foreign country, which is exactly the same:
it has the same demand curve and there is only one firm there that also produces apples at the
marginal cost of $4 per kilo. Also, each firm in every country has to pay a transportation cost of
$1 per kilo to deliver its apples to the market abroad.

A) In the trade equilibrium, calculate the prices in both countries.

Explanation / Answer

dC/dQ = 4
=> C = 4Q
Profit  = PQ - C
= 20Q -2Q^2 - 4Q
for maximum profit d/dQ = 20-4Q-4 = 0 => Q =4

=> P = 20-4x4 = 4

In 2nd country,

dC/dQ = 4+1 = 5
=> C = 5Q
Profit  = PQ - C
= 20Q -2Q^2 - 5Q
for maximum profit d/dQ = 20-4Q-5 = 0 => Q =3.75

 

=> P = 20-4x3.75 =15

 

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