Question

3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ??? = 1.8? −0.7? 0.6 and ??? = 3.6? 0.3? −0.4 . a. In the short run assume that capital is fixed at ? = 10. Derive formulas for the short-run Total Product (TP), Average Product (APL), and Marginal Product (MPL). Graph these three functions. b. In the long run, capital is not fixed. Graph the isoquant for ? = 6. Identify and label three points on the isoquant. (You’ll need to do some math here.) c. Calculate the MRTS. d. Use the MRTS formula to determine the slope of the isoquant at the three points you identified. Label the slopes at these points.

4) Consider the production function ? = ? 1.5 + 4?. a. Starting from the input combination (9,5), calculate the marginal product of adding one worker. b. What is the marginal product of adding another worker? c. Is the marginal product of labor increasing or decreasing?

5) Consider the production function ? = √? + 7? 3 . Starting from the input combination (2,5), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?

6) Do the following functions exhibit increasing, constant or decreasing returns to scale? What happens to the marginal product of labor as labor is increased and capital is held constant starting from the input combination (20,20)? a. ? = 3? + 8? b. ? = 4? 2? c. ? = 3? 0.4? 0.3

Answer 1

Figure 1

Figure 2

Table 1

Points	L	K
A	1	1
B	4	0.5
C	16	0.25

Table 2

Slope	Value
1	-0.5
2	-0.0625
3	-0.00781