4. (25 points) A monopolistically competitive company assembles and installs sol

Question

4. (25 points) A monopolistically competitive company assembles and installs solar panels it imports at $10 per unit. All remaining costs of the company, denoted RC, is given by the following (where Q is a unit of solar panel): RC(Q) 1,000+5Q2 The demand faced by this company is given by P=500-30Q. a) (10 points) What is the optimal production level, Q, and what is the profit at Q*? b) (15 points) US announced on Jan 22, 2018 that, a tariff (tax) of 30% would be imposed on imported solar panels. (https://www.forbes.com/sites/davekeating/2018/01/23/trump-follows-europes-lead with-Chinese-solar-panel-tariffs/#7d7b055931a8) Assuming demand stays the same, what would be the new Q' and (Q*)? (According to the article, various aspects of solar industry is going to be affected but for the purposes of this question, consider only the change in imported solar panel price)

Explanation / Answer

a) Total cost for a typical firm is RC = 1000 + 10Q + 5Q^2. Each firm in the market equates MC with
MR
MC is 10 + 10Q and MR is 500 - 60Q. Find Q*
500 - 60Q = 10 + 10Q
490 = 70Q
Q* = 7 and price P* = 500 - 30*7 = $290.
The profit for a typical firm is Revenue - cost
= 7*290 - (1000 + 10*7 + 5*(7^2)) = $715
b) When imports are charged a tariff of 30%, the new price for import is $10 + $10*30% = $13 per Q.
Total cost now is RCNew = 1000 + 13Q + 5Q^2.
MC is 13 + 10Q and MR is 500 - 60Q. Find Q*
500 - 60Q = 13 + 10Q
487 = 70Q
Q* = 6.957 and price P* = 500 - 30*6.957 = $291.29.
The profit for a typical firm is Revenue - cost
= 6.957*291.29 - (1000 + 10*6.957 + 5*(6.957^2)) = $715 (approx)
The tariff has no impact on the profit levels because the profits are unchanged.

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