PS 07 - L(Hint K and L will be functions of q v and w b...

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L2: Preferences & Utility I Problem Set #7 Costs 1) Suppose a firm has a two-input ( K,L ) linear production function, a) Show that the cost-minimizing amounts of K and L will generally require the use of only K or L . b) Calculate the firm’s marginal cost function and average cost function? [ Remember that cost functions are functions of quantity. ] 2) Suppose the firm’s production function is q = min[ 5K,10L ] and the rental rates of capital and labor are v = 1 and w = 3, respectively. a) What is the firm’s long-run total cost function? b) What is the firm’s short run total cost function if K = 10? 3) Suppose the firm’s production function is where α, β > 0 and where the firm can purchase all the K and L it wants in competitive input markets at input costs of v and w , respectively. a) Solve for the cost-minimizing values of K and L b) Derive the long-run total cost function c) Calculate MC 4) Start with the following production function: a) Calculate the cost minimizing amounts of K and
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Unformatted text preview: L (Hint: K * and L * will be functions of q, v and w ) b) Compute the TC function (Hint: TC will be functions of q, v and w ) c) Compute the TC function if w = v = $4. (Hint: TC will now be function only of q ) d) If K is fixed at K 1 , then the production function is: Show that the STC function is : For the remainder of question (4) assume K 1 = 4 and if w = v = $4. e) Calculate the short-run marginal cost . f) Calculate the firm’s short-run variable cost function and the short-run average variable cost function. g) What is the firm’s shut-down price? (Hint: Think about average variable costs) h) Calculate the firm’s short-run average total cost function. i) At what price with the firm break even? j) Will the firm produce in the short run if the price is $0.60? Why or why not? 5) Is the elasticity of SAFC with respect to q larger at high output levels or at low output levels? Dr. Steven Waters Econ 380 Page 1 of 1...
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