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Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...

Consider the production function given by
y = f(L,K) = L^(1/2) K^(1/3) ,

where y is the output, L is the labour input, and K is the capital input.

(a) Does this exhibit constant, increasing, or decreasing returns to scale?

(b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function?

(c) Determine whether the short-run production function exhibits diminishing marginal product of labour.

(d) In the long-run, both inputs are variable. Find the marginal rate of technical substitution (MRTS). If the firm employs L = 15 and K = 20, what does the MRTS tell you?

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Answer #1

5 R preduchion c) Differentiating y μ驰 spect to L, dレ 2ル

LuPL dレ dy 21なヤ 33 2L 20, L-t) 2x15 Lovel frxed, it we asttoby ome nit keeping fe eutrut sh Catitnl 0 ㄧㄥ

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