Question 3 (10 Total Marks) A firm has the following production function, Q=2K$^rac{1}{2}$L$^rac{1}{2}$ The profit maximizing firm faces the problem of producing the optimal amount of output Q, with a budget constraint of $30,000. If P?=$3 and P?=$6, what are the optimal amounts of capital and labour that this profit-maximizing firm should use? (4 marks) What is the optimal amount of output? (4 marks) Illustrate your answer. (2 marks) K L
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Step 1: Determine the production function The given production function is 7x^2 = 0, where x represents the amount of output Q. Show more…
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Consider a firm with a production function: Q(L,K) = 400 + 12.3L - 0.8L^2 + 10.1K - 0.3K^2 + 0.2LK, Where a firm employs K units of capital and L units of labour. Q describes the output which the firm can produce with these inputs. Assume that the firm is a price taker in the product market and in both factor markets. If P = 10 is the price of the commodity produced, r = 1 the interest rate and w = 3 the wage rate, then find maximum profit ̠́(L, K) of this firm. Hint. The maximum profit ̠́(L, K) of the firm with P - price of the commodity produced, r - the interest rate and w - the wage rate ̠́(L, K) = P · Q(L, K) - rK - wL
Sri K.
Consider the following production function for a firm: q = 200L^0.75 K^0.25 where q = output, K = capital and L = labor. The firm uses capital and labor whose prices are $60 and $30 respectively. The total cost outlay for the utilizations of both capital and labor is $8,400. Using the Lagrangian Multiplier procedure, determine the amount of each input to use, which will maximize output.
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