A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function?   (b) Derive the marginal product of labor and capital.   (c) What do we mean when we say the production function is linearly homogenous?

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Given the following production function: q = 10KL. Assume that w = 25, r = 75 and C = 1200. (a) Mathematically find the minimum cost combination of capital and labour to produce a given level of output.b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain.  (c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate, assuming the firm is producing at the same level of output.

Which of the following production function would exhibit increasing returns to scale? f(K, L) = (K+ L)1/2 f(K, L) = K + L f(K, L) = K1/4+ [1/4 Of(K, L) = KIL None of the above

How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?

Which of the following production functions exhibits increasing returns to scale in the factors of production K and L? a. y = ĀK0.3 L0.75 b. y = Kª(ĀL)-e,0 < a < 1 c. y = ĀKO.3L0.3 d. y = ĀK/4 + L³/4

Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale

oj Consider the Cobb-Douglas production function P(L, K) = 6L0.6 K04_ Find the %3D total units of production when 19 units of labor and 12 units of capital are invested.

How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?