A firm is required to produce 48.0 units of output using quantities of labor and capital (L, K) = (3, 12). For each of the following production functions, state whether it is possible to produce the required output with the given input combination. If it is possible, state whether pro - ducing Q = 48.0 with input combination is technically efficient or inefficient. (a) Q=9L + 5K (b) Q=4KL + L - 6. (c) Q=8 KL (d) Q = min {14L, 2K}

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Pugh

16 February, 21:13

A firm is required to produce 48.0 units of output using quantities of labor and capital (L, K) = (3, 12). For each of the following production functions, state whether it is possible to produce the required output with the given input combination. If it is possible, state whether pro - ducing Q = 48.0 with input combination is technically efficient or inefficient. (a) Q=9L + 5K (b) Q=4KL + L - 6. (c) Q=8 KL (d) Q = min {14L, 2K}

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Fisher · Answer 1

The problem requires replace the input of labor and capital in the respective functions and compare the output with 48 (required units).

(a) Q=9L + 5K with the input (L, K) = (3,12) gives

Q = 9*3 + 5*12 = 27+60 = 87 so the production of 48 units is feasible but inefficient. It is produced more units than required.

(b) Q = 4KL+L-6

Q = 4*12*3 + 3 - 6 = 141 so, the production of 48 units is feasible but so inefficient.

(c) Q = 8KL

Q = 8*12*3 = 288 the production of 48 units is feasible but very inefficient.

(d) Q = min{14L, 2K}

Q = min{14*3, 2*12} = min{42, 24} = 24 (the minimum value between 42 and 24). So, the production of 48 units is not feasible with this production function and the given input.