Show full answers and steps to part d) e) & f) Consider a firm with production function:LK3(a)Find the marginal product of labor,MPL. Next, indicate whether marginal product oflabor is decreasing, constant, or increasing inlabor. Explain or show your answer.(b)Find the marginal product ofcapital, MPK. Next, indicate whether the marginalproduct of capital is decreasing, constant, orincreasing in capital. Explain or show your answer.(c)Find and simplify the expression of themarginal rate of technical substitution of labor forcapital, MRTSL.K. Next, indicate whetherMRT SL,K is decreasing, constant orincreasing in labor, and explain what does that thisMRTSL,K suggest about the shape of theisoquants and the firm's ability to substitutebetween inputs.(d)] Show whether the firm's productionfunction exhibits increasing, decreasing, orconstant returns to scale.< (e) ₁Suppose the firm operates in the shortrun: Capital is fixed at 24. Solve the firm's costminimization problem (CMP) to find the inputdemand of labor for any output level q in the shortrun.(f) [} Assuming inputs prices arew =: $4 (price of labor) and r = $3 (price ofcapital), use your answer in part (e) to find theoptimal amount of labor the firm uses to produce256 in the short run. Next, find the simplifiedexpression for the firm's short-run total cost9=curve/function and calculate the minimized totalcost of producing the output target.

Production function: Here q denotes the level of output produced using labor L and capital K. In the…

(e) ₁ Suppose the firm operates in the short run: Capital is fixed at 24. Solve the firm's cost minimization problem (CMP) to find the input demand of labor for any output level q in the short run. (f) [ 1 Assuming inputs prices are W= $4 (price of labor) and r = $3 (price of capital), use your answer in part (e) to find the optimal amount of labor the firm uses to produce 9 256 in the short run. Next, find the simplified expression for the firm's short-run total cost curve/function and calculate the minimized total cost of producing the output target. =

(e) ₁ Suppose the firm operates in the short run: Capital is fixed at 24. Solve the firm's cost minimization problem (CMP) to find the input demand of labor for any output level q in the short run. (f) [ 1 Assuming inputs prices are W= $4 (price of labor) and r = $3 (price of capital), use your answer in part (e) to find the optimal amount of labor the firm uses to produce 9 256 in the short run. Next, find the simplified expression for the firm's short-run total cost curve/function and calculate the minimized total cost of producing the output target. =

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section7.A: Appendix: A Closer Look At Production And Cost

Problem 1AQ

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