Question

Given the Cobb-Douglas production function for Mabel’s factory

Q = (L0.4) * (K0.7)

a) Based on the function above, does Mabel’s factory experiencing

economies or diseconomies of scale? Explain.

b) If the manager wished to raise productivity by 50% and planned to

increase capital by 25%, how much would she have to increase her labor

to reach that desired production level?

Answer 1

Q=L^0.4*K^0.7

Above function is Cobb Douglas of form Q=L^(alpha)*K^(beta) and if alpha+beta>1 then increasing return to scale and alpha+beta=1 then constant return to scale; alpha+beta<1 then decreasing return to scale

In our case 0.4+0.7=1.1>1

ANswer for b)

New Q=1.5*Old Q

New K=1.25* Old K

New Q=(New K)^0,7*(New L)^0.4

Old Q=K^0.7*L^0.4

New K)^0,7*(New L)^0.4=1.5*K^0.7*L^0.4

(1.25*K)^0.7*(New L)^0.4=1.5*K^0.7*L^0.4

New L^0.4=(1.5/1.2)^0.7*L^0.4

New L^0.4=1.17*L^0.4

New L=1.17^(0.25)*L

New L=1.04*L

Hence Labor should be increased by 4%