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 = KL €“ (0.1) 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 10. Fill in the following table.
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.
c. Now suppose that K increases to 20 because the firm increases the size of its widget factory. Re-compute the value of Q for each of the alternative values of L. Plot the values of Q and 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).