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Assume a firm has the following production function: F(K,L)=L+(1+K)^(1/2) where L and K represent the inputs labor and capital.
A. Show a derivation for the MRTSLK.
B. Does this production function have declining MRTSLK? Be sure to show your work.
C. Does this production function have increasing, decreasing, or constant returns to scale?
D. Which input bundle represents efficient production of 100 units of output if the rental paid to capital is $25 and the wage paid to labor is $50? Round any decimals to the nearest hundredth.
E. Derive the firm's cost function using the rental and wage listed in Part D.
F. Does this firm exhibit economies or diseconomies of scale?
G. What is the firm's efficient scale of production?
At what output is the average variable cost (AVC) at a minimum and if the market price of the firm's output is $7.5 per unit, should the firm produce or shut down?
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