30 Apr Question: Derive the cost function associated with the production function in questions 2 is C(q) = 4 + 2q …
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
Instructions: In the problems that follow, you are asked to find the efficient combinations of capital (K) and labor (L) to produce the desired quantity of output at minimum cost. The price of capital is denoted by r and the price oflabor is denoted by w. 3. Let the production function be given by Q KL with r -2 and w-1. [Note (marginal product of capital) MPk -L and (marginal product of labor) MPL K. a) → How much K and L is employed in the efficient production of 32 units of output? v Since given output is 32 units, then using Equation (1), the given output function is rewritten as followsu 32-KL L-32/K, Thus, required labor for production 32 units output is L-32/K» Now, using Equation (2), substituting with respective given information, the required function is as follows KL=1.2+’ On comparing both results, the required capital is- L-2K 32/K-2K 16 K2 Thus, the required capital is 4 units and labor is 8 unitsv b) What is the minimum cost ofproducing 32 units of output?» The total cost of production of 32 units of outputs is C-wItrK-1*8+2*4-16v Thus, the total cost of 32 units of output is 16. c) → Show your results graphically.
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