Question

Suppose a firm has a fixed-proportions production function, in which one unit of output is produced using two workers and one unit of capital.

a. Draw the isoquants for this production function, representing labor on the x-axis and capital on the y-axis.

b.Define and show the expansion path of the firm.

c. Suppose capital is fixed at three units. Show, by means of a line on the diagram, the short run possibilities of combining workers and capital when workers go from zero to 12. Explain.

d.Draw the total product of labor (short run production function), the average product of labor and the marginal product of labor when workers go from zero to 12 and capital is fixed at 3. Explain a little the diagrams.

PLEASE DRAW THE DIAGRAM, THEY ARE REALLY IMPORTANT FOR ME

Answer 1

a.

b.

c. Below is the short run production schedule when capital is fixed at 3 units -

K	L	Y= Min(L/2,K)
3	0	0
3	2	1
3	4	2
3	6	3
3	8	4
3	10	5
3	12	6

Below are excel formulas for reference -

d.

Average Product of Labor = TP/L while marginal product of labor is calculated by change in total product divided by change in labor.

K	L	Y= Min(L/2,K)	AP	MP
12	0	0
12	2	1	0.5	0.5
12	4	2	0.5	0.5
12	6	3	0.5	0.5
12	8	4	0.5	0.5
12	10	5	0.5	0.5
12	12	6	0.5	0.5

MP and AP curve overlap on each other -

The marginal product and average product of labor for a fixed proportions production function are constant across different levels of labor. Hence, they overlap each other in the above diagram.

Below are excel formulas for same -