Question

Derive the cost function associated with the production function in questions 2 is C(q) = 4 + 2q and in questions 3 is C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) = xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given by C(g) -10q? Explain your answer carefully.. A monopolist or a perfectly competitive fim maximizes profit at the point where arginal revenue equals marginal cost Revenue Price x quantity* Revenue- (20-9q Marginal revenue - 20 - 2Q A monopolist has a cost function of C-4 2q Marginal cost2 Equating marginal revenue and marginal cost 20 - 2Q-2 Q-9 unitsv price 20-9 Price -S 11 Thus a monopolist charges a price of S 9.v For a perfectly competitive firm, the cost 10Q Marginal cost 10 Equating marginal revenue and marginal cost 20- 2Q-10 Q-5 unitsv Price-20-Q Price 20-5 Price -S 15 Thus the consumers would prefer to face a monopolist than a perfectly competitve fim because the price charged by the monopolist is less than the price charged by the perfectly competitive firm.v

Answer 1

Answer to question 2 is wrong , so it is rectified and correct answer is provided below . Please post one question at a time .

Monopoly c(q) = 4 + 2 q MC = delta C/delta q = 2 TR = P times Q = (20 minus q) q = 20 q minus q^2 MR = delta TR/delta q = 20 minus 2 q MR = MC rightarrow Profit Max = 20 minus 2 q = 2 = q = 18/2 = 9 units P = 20 minus q = 20 minus q = 11 $ Perfect completion MR = P = MC Production point MC = delta TC/delta q [TC = 10 q] = 10 P = 10 = 20 minus q = 10 = q = 10 units P = 20 minus q = 20 minus 10 = 10 $ Monopoly: p P = 11 $ PC: - P = 10 $ People will prefer PC then monopoly since monopoly price is higher.