Use the following lo answer questions (1) though (6) Suppose a Ann produces acco

Question

Use the following lo answer questions (1) though (6) Suppose a Ann produces according to the following production function; Q= K + I., where Q is the quantity produced, K is the amount of capital employed, and L is the number of workers employed. Suppose price of the firm's output is 100. the price of capital it 10. and the pnoe of labor is 20 Initially operating in the short run. with K fixed at 5. the marginal revenue product of the 2nd unit of equals: 200 100 20 5 Now imagine the firm is operating in the long run, with both K and L variable. With K on the vertical axis and L on the horizontal axis, if the firm desires to produce 100 units of output, then the marginal rate of technical substitution (MRTS) at K - 50 and L = 50 equals -50 -2 -1 None of the above With K on the vertical axis and I. on Ihc horizontal axis, the slope of any particular iso cost line for this firm equals

Explanation / Answer

Q = K + L

Total cost, TC = wL + rK

TC = 20L + 10K

[1] K = 5

Q = L + 5

TR = P x Q = 100 x (L + 5) = 100L + 500

MR = dTR / dL = 100

MPL = dQ / dL = 1

MRPL = MPL x MR

= 1 x 100 = 100

Option (B)

[2]

MPL = 1

MPK = dQ / dK = 1

MRS = - (MPL / MPK) = - 1 irrespective of values of L & K (This is because the production function is additive, indicating that L & K are perfect substitutes).

Option (C)

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