2) Barley is produced according to the production function, Q = 100(K0.8 L 0.2)

Question

2) Barley is produced according to the production function, Q = 100(K0.8 L 0.2)

a) Consider the short run: beginning with a capital input of 4 (fixed) and a labor input of 35 (varying), show and explain whether the marginal product of labor is increasing, decreasing, or constant. That is, what is the MPL for L = 35 to 40 (in increments of whole units of labor).

b) Consider the short run: beginning with a capital input of 4 (varying) and a labor input of 35 (fixed), show and explain whether the marginal product of capital is increasing, decreasing, or constant. That is, what is the MPK for K = 4 to 9 (in increments of whole units of capital).

c) Would you expect the pattern in parts a and b to change for larger values? Explain. (Hint: what would a sketch of the function look like in each case?)

d) Consider the long run: Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain. (Hint: what happens to output when inputs are doubled? Tripled? Increased ten-fold?)

Explanation / Answer

a) K L Q MPL 4 35 617.2507 4 36 620.7382 3.487514 4 37 624.1491 3.410855 4 38 627.487 3.337886 4 39 630.7553 3.268338 4 40 633.9573 3.201968 b) MPL is decraesing. MPL = Q36-Q37 and like wise. K L Q MPL 4 35 617.2507 5 35 737.8866 120.6359 6 35 853.7577 115.8711 7 35 965.8108 112.0531 8 35 1074.696 108.8852 9 35 1180.885 106.1891 MPK is also decraesing with incraese in employmnt of capital keeping Labor constant. c) The fall in the Marginal product will be more for larger values. This is because to increase output further when one of the input is fixed a huge incraese in the employment will lead to only small changes in the output. d) In long run the Production function exghibit constant returns to scale.In long run both the inputs can be varied. If we varry the inputs by the same proportion t then the output also rises by the ssame proprtion t. Q(K, L) = 100K^0.8L^0.2 Q(tK,tL) = 100(tK)^0.8(tL)^0.2 100(t)^0.8K^0.8*t^0.2*L^0.2 t*100K^0.8*L^0.2 t*Q(K,L) Thus CRS.

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