consider the following Cobb- Douglas production for red bean coffee. q=(l^0.2)*(

Question

consider the following Cobb- Douglas production for red bean coffee. q=(l^0.2)*(k^0.5)

a. intutively, why are cobb-douglas production function more appropriate representations of reality than, say, linear production functions ?

b. based on the function above, is red bean cofee's business experiencing economies or diseconomies of scale? explain how uou arrived at your answer.

c. if red bean cofee decided to boost labor by 15% and captail by 10%, how much will productivity increase?

d. if red bean cofee wanted to boost productivity by 40% and already knew they were going to increase captail by 20%, how much would they have to increase their labor force to rach this production targer?

Explanation / Answer

a  cobb-douglas production function are more appropriate representations of reality than, say, linear production functions because In reality the shares of labor and capital of total output could be constant over time and Cobb Douglas functions can easily show that while Linear functions can't show the same.

b. red bean cofee's business experiencing diseconomies of scale as increase of output is less when is each input is increased by the lamda. this can be shown as

  q = (L)^0.2*(k)^0.5

   = ^0.2(L)^0.2*()^0.5(k)^0.5

   = ^0.7(L)^0.2*(k)^0.5

So, q > ^0.7*q

Hence diseconomies of scale

c. Increase in productvity = 7.8%

as Productivity = change inoutput due tochange in Labour and capital

so = (1.15L)^0.2(1.1K)^0.5 = 1.078(L)^.2(K)^.5

d. 1.40Q = (L+l)^0.2(1.2K)^0.5

(L+l)^.2 = 1.40/1.095

= (1.278)^5

l = 3.409 -1

l = 2.409

So change in Labour would be 240.9%

If you don't understand anything then comment, I'ill revert back on the same.

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