Question

A firm's market demand for its product in the company’s country, a, is given by Qa(Pa) = 1,050 − 4Pa, where Qa is the quantity of products produced per year and Pa is the price product. Cost of producing this product is ?(Q) = 70,125 + 0.0125Q2. This implies a marginal cost of production of ?C(q) = 0.025Q.

a) Find the profit-maximizing price and quantity. Compute the firm’s profit in this case. Should the firm shut down in the short run?

Suppose the company succeeds in obtaining approval for selling its product in country b. Market research suggests that the demand for the product in this new market is

Qb(Pb) = 1,400 − 16Pb.

b) The firm decides to treat the two countries as different segments. Find the optimal price the firm should charge in the country “a” and the optimal price it should charge in-country “?”. What will the firm’s profit be in this case?[Assume legal protections are in place that prevents reimportation into country a]

c)The government in the country “a” legalizes reimportation. How does that change the firm's optimal pricing strategy? Who will lose out as a result?

Answer 1

Maakel demand for the product in courthy 'a' ïs - Calpa) = 1050-4Pa - Pa, sepresents quantity demanded and Pa is the frice of the padducts, Jaype) bepaesehats quantity as a function of ginen cost of producing the product & C(Q) 270,125 + 0 - 2) MC (8) = 0.0250.

al. In perfect in compen in perfect competition, the firm can shut down shoid-run where as in monoflly It doen not haffen so. Thus to find propt manining Alle and quality Price marginal Cost or P. Mc. - (1) Pappa) 400 - loso) 11050 - Pa) 71 According to cq (1) floso - Qa';' 0.025 R. 2) 1050-Q a 0.10 2) 0 ₂ 954.54 » Profil maninising quantity is 954.54

Now Price can be found by substitutup 8 95mos u in eq (11) 1 (1050- 954.54) apa 2) Par 23.865 Isopit monimuising price 'n 23.865 Yo sind Profit sahtract Price and Avc Murage variable cost. AVC = 0.012582/Q - - 0.0125 68 -0.0125 x 954.54 11.9317 P-AVC2 23.865-11.9317 311.9335 : The frice of a unit commodity in greater than AVC by 11.933 müh. Hence the profit is 11.933 units Sunce from us caning profil, it should not shut down.

DOMS Now Price can be found by sunsfituting Q 2954354 in eq (1) I (1050 - 954.54) apa 2) Pa 23.865 Profit manumising price is 23.865 To find Profit sahtract Price and AVC (Average variable cost, AVC = 0.0125Q²Q " = 0.0125 -0.0125 x 954.54 11.9317 P-AVC2 23.865-11.9317 2 11.9335 . The price of a unit commodity is greater than AVC by 11.933 cuil. Hence the profit is 11.933 units a sunce firm us caming profit, it should not shut down.