A firm’s short run production function is believed to be of the form: Q = AL^n?

Question

The following table gives data relating to a firm’s output Q and labour L.

L 1 2 3 4 5

Q 0.50 0.63 0.72 0.80 0.85

1. Show that lnQ = n ln L + ln A.

2.write up a table of values ln L and ln Q

3.estimate the values of the parameters n and A and hence write down the approximate relation between Q and L

Answer 1

So what's the problem?

If you have a spreadsheet program (Open Office, Excel, Numbers, etc.), put the L values in one column, say A; put the Q values in a second column, say B; and the logs of L and Q in columns C and D respectively.

Plot ln Q as a function of ln L (scatter plot) and ask the program to give you a linear fit, displaying the equation.

The linear fit will be an equation of the form kX +b.

The k is your n, the b is your ln A.

If you can't use a computer, then with only 5 points, you can do it with a graphing calculator or by hand, but you should get access to a spreadsheet program ASAP.