Question

The table below gives the amount of output/total product (TP) that a firm can produce with various combinations of labor (L) and capital (K):

K L TP AP MP

10 4 91 29

10 5 121

10 6 150

10 7 175

10 8 197

10 9 212

10 10 217

10 11 215

a. Is the above production function a short run or long run production function? EXPLAIN why.

b. Complete the table by computing the average product (AP) and marginal product (MP) of labor.

c. With which unit of labor is maximum production efficiency achieved? Why is this the point of maximum production efficiency? d. With which unit of labor is diminishing marginal returns confronted? Why is this the point of diminishing marginal returns?

e. With which unit of labor does Stage II of Production begin? With which unit of labor does Stage II of production end?

try to do all pls and thank you

Answer 1

a. Is the above production function a short run or long run production function? EXPLAIN why.

The production function is a short-run production function. IN the short run there is a fixed and variable factor of production whereas in long run there is no fixed factor of production. Labor and capital are factors of production here. A fixed factor of production does not vary with output (total production) whereas a variable factor of production does. Here level of capital stays constant at 10 units irrespective of the level of production – hence fixed factor of production. Whereas the level of labor varies with the level of output, hence the variable factor of production.

b. Complete the table by computing the average product (AP) and marginal product (MP) of labor.

K	L	TP	AP	MP
10	4	91	22.8	29
10	5	121	24.2	30
10	6	150	25.0	29
10	7	175	25.0	25
10	8	197	24.6	22
10	9	212	23.6	15
10	10	217	21.7	5
10	11	215	19.5	-2

AP = TP/ L for each level of L

And MP = change in TP/ change in L (for ex (121-91)/(5-4) = 30)

c. With which unit of labor is maximum production efficiency achieved? Why is this the point of maximum production efficiency?

The point of maximum production efficiency occurs when the short-run average cost curve is minimum. The short-run average cost is minimum when the average production curve is maximum and equal to the marginal product. In the given scenario it happens at L=7. At this point AP=MP=25. This is the point where the product is produced at lowest possible cost. The average product of labour measures labor productivity. Labour productivity is maximum at L=7, after that point each unit of labour costs more since its productivity declines. Making production at that point most efficient.

d. With which unit of labor is diminishing marginal returns confronted? Why is this the point of diminishing marginal returns?

The Law of diminishing marginal returns means every additional unit of input would lead to a smaller increase in output. In other terms, the marginal product of the input is declining. As we can see from the table this happens when we employ the 6^th unit of labor, the marginal product of labor declines from 30 to 29. This happens because more units of labor are employed per unit of capital hence bringing down the productivity of each additional labor.

e. With which unit of labor does Stage II of Production begin? With which unit of labor does Stage II of production end?

Stage 2 production lies between the point from which AP declines to the point at which MP becomes 0. Hence At L=7 stage II begins and at L=10 stage II ends. At L=11, MP is negative, hence we took L=10 as the endpoint of stage II.