Question

2. (40 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 (as a function of per unit solar panel): RC(Q) = 1,000+5Q2 The demand faced by this company is given by Q-16.67-xP where P denotes the price, Q denotes the quantity and x is currently equal to 1/30. 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- Assuming demand stays the same, what would be the new Q* and Π(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) c) (15 points) What would be x in the long run?

Answer 1

Total cost (TC) = RC + Total cost of import = 1,000 + 5Q² + 10Q

Marginal cost (MC) = dTC/dQ = 10Q + 10

(a) Q = 16.67 - (P/30)

30Q = 500 - P

P = 500 - 30Q

Profit is maximized when Marginal revenue (MR) equals MC.

Total revenue (TR) = P x Q = 500Q - 30Q²

MR = dTR/dQ = 500 - 60Q

500 - 60Q = 10Q + 10

70Q = 490

Q = 7

P = 500 - (30 x 7) = 500 - 210 = 290

TR = 290 x 7 = 2,030

TC = 1,000 + (5 x 7 x 7) + (10 x 7) = 1,000 + 245 + 70 = 1,315

Profit = TR - TC = 2,030 - 1,315 = 715

(b) The 30% tariff will increase the cost of import by 30%, so import cost per unit will be ($10 x 1.3) = $13.

New TC = 1,000 + 5Q² + 13Q

New Marginal cost (MC) = dTC/dQ = 10Q + 13

Equating with MR,

500 - 60Q = 10Q + 13

70Q = 487

Q = 6.96

P = 500 - (30 x 6.96) = 500 - 208.8 = 291.2

TR = 291.2 x 6.96 = 2,026.75

TC = 1,000 + (5 x 6.96 x 6.96) + (13 x 6.96) = 1,000 + 242.21 + 90.48 = 1,332.69

New profit = 2,026.75 - 1,332.69 = 694.06

(c) Long run demand function: Q = 16.67 - xP

xP = 16.67 - Q

P = (16.67 - Q)/x

TR = P x Q = (16.67Q - Q²)/x

MR = dTR/dQ = (16.67 - 2Q)/x

In long-run monopolistically competitive equilibrium, MR = MC and P = ATC.

(16.67 - 2Q)/x = 10Q + 10

x = (16.67 - 2Q)/ (10Q + 10)........(1)

ATC = TC/Q = (1,000/Q) + 5Q + 10

Equating ATC and MC,

(1,000/Q) + 5Q + 10 = 10Q + 10

1,000/Q = 5Q

Q² = 1,000/5 = 200

Q = 14.14

Substituting in (1),

x = [16.67 - (2 x 14.14)] / [(10 x 14.14) + 10]

x = (16.67 - 28.28) / (141.4 + 10)

x = -11.61 / 151.4

x = -0.0767