The Cobb-Douglas production function is: Q = 1.4*L^0.6*K^0.5.What would be the percentage change in output (%∆Q)if labor grows by 3.0% and capital is cut by 5.0%? [Hint: %∆Q = (E_L * %∆L)+ (E_K * %∆K)]

Question

Quizplus · Accepted Answer

Using the given formula: %∆Q = (E_L * %∆L) + (E_K * %∆K) E_L = 1.4*(1.0^1)*1.0^0.6*(1.0)^0 = 1.4 E_K = 1.4*(1.0^1)*1.0^0.5*(-0.05)^1 = -0.098 %∆L = 3% %∆K = -5% Substituting the values: %∆Q = (1.4*3%) + (-0.098*5%) = 0.042 - 0.005 = -0.037 = -0.70% Therefore, the percentage change in output would be -0.70%. The correct answer is option C.

The Cobb-Douglas Production Function Is: Q = 1