Consider an example of a production function that relates the monthly production of widgets to the monthly use of capital and labour services. Suppose the production function takes the following specific algebraic form:

Q = K *L - (0.15) *L²

Where Q is the output of widgets, K is the input of capital services, and L is the input of labour services.

a.Suppose that, in the short run, K is constant and equal to 15. Feel in the following table

K

L

Q

15

5

?

15

10

?

15

15

?

15

20

?

15

25

?

15

30

?

15

40

?

15

50

?

B. Using the values from the table, plot the values of Q and L on a scale diagram, with Q on the vertical axis and L on the horizontal axis. (This is analogous to the TP curve).

C. Now suppose that K increases to 25 because the firm increases the size of its widget factory. Re-compute the values of Q for each of the alternative values of L. Plot the values of Q an L on the same diagram as in part (B)

D. Explain why an increase in k increases the level of Q (for any given level of L).