Question

12.       Suppose an economy's production function is specified by y = A(√K,√L), where A represents the productivity of resources, K the quantity of capital resources, and L the quantity of labor resources.

            A. Find potential output when A = 10, K = 49, and L =9.

            B. Find potential output when A = 10, K = 49, and labor resources are 3, 6, and 12.

            C. Plot the levels of output associated with 3, 6, 9, and 12 labor units; label the production function P'. What happens to this production function when productivity increases (the value of A is larger) and/or there is more capital?

Answer 1

A. Potential output when A = 10, K = 49, and L =9.

Y = A(√K.√L)

put the values

Y= 10 (√49.√9)

Y= 10. 7. 3

Y= 210

B. Potential output when A = 10, K = 49, and labor resources are 3, 6, and 12.

Y = A(√K.√L)

When L=3

Y = 10 (√49.√3)

Y= 10(7)(1.73)

Y= 121.1

When L=6

Y = 10 (√49.√6)

Y= 10(7)(2.44)

Y= 170.8

When L=9

Y= 210 (Solved in part A)

C) This Red Line is Production Function P'.

When productivity increases (the value of A is larger) and/or there is more capital the production Function shifts up. Because at the same level of capital and labour the productivity has increased.