Consider a firm whose technology is given by the production function: y = f (K,L) = (N+1)L + 2√ K. Assume that input prices for labour, L, and capital, K, are w = 1 and r = 2 respectively. a) Find the firm's short run total cost function assuming the firm cannot hire more workers nor fire its only worker, i.e. L = 1 is fixed. b) Find the firm's short run marginal cost, average variable cost and average fixed cost. Draw the three of them in the same graph. What is the short-run supply of the firm? c) Find the firm's long run total cost function, i.e. when all factors are variable. d) Find the firm's long run marginal cost and average cost. Draw them in the same graph. What is the long-run supply of the firm?
Consider a firm whose technology is given by the production function: y = f (K,L) = (N+1)L + 2√ K. Assume that input prices for labour, L, and capital, K, are w = 1 and r = 2 respectively. a) Find the firm's short run total cost function assuming the firm cannot hire more workers nor fire its only worker, i.e. L = 1 is fixed. b) Find the firm's short run marginal cost, average variable cost and average fixed cost. Draw the three of them in the same graph. What is the short-run supply of the firm? c) Find the firm's long run total cost function, i.e. when all factors are variable. d) Find the firm's long run marginal cost and average cost. Draw them in the same graph. What is the long-run supply of the firm?
Chapter22: Supply: The Costs Of Doing Business
Section: Chapter Questions
Problem 11E
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Transcribed Image Text:Consider a firm whose technology is given by the production function: y = f (K,L) = (N+1)L + 2√
K. Assume that input prices for labour, L, and capital, K, are w = 1 and r = 2 respectively. a)
Find the firm's short run total cost function assuming the firm cannot hire more workers nor
fire its only worker, i.e. L = 1 is fixed. b) Find the firm's short run marginal cost, average
variable cost and average fixed cost. Draw the three of them in the same graph. What is the
short-run supply of the firm? c) Find the firm's long run total cost function, i.e. when all factors
are variable. d) Find the firm's long run marginal cost and average cost. Draw them in the
same graph. What is the long-run supply of the firm?
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