Suppose qAK13 L23 and wv5 a Find the long run total cost cur

Suppose q=AK^(1/3) L^(2/3) and w=v=5. (a) Find the long run total cost curve. Then briefly explain (b) what A is and why an increase in A lowers total costs.

Solution

q=AK(1/3) L(2/3) where w=v=5

k= 9q/ 2AL , L= 9q/2AK

long run total cost curve

TC= wL + vK

= 5 (9q/2AL ) + 5(9q/2AK)

= 45 q /2A(1/L+1/K)   

b.A is total factor productivity it, is a variable which accounts for effects in total output not caused by traditionally measured inputs of labor and capital.It is a positive constant.it is a long term technological change thats why an increase in A lowers total costs..