Question

(c) ()The average product of labour when three workers farm an acre of land is 150 bushels of wheat and the marginal product. when fourth worker is employed. is 75 bushels. What is the total output with four workers? (i) What is the minimum efficient scale of production in long-run average cost? (i) Determine whether the following production functions exhibit increasing, decreasing or constant returns to scale: Q = 300K + 25L 2+2+2

Please solve the above sum

Answer 1

Answer c (i) Total product with 4 workers is 525

	Total product/Number of workers	dTotal Product/dWorkers
Worker	Average Product	Marginal Product	Total Product
3	150		450
4	131.25	75	525

Average Product = Total product/Number of workers

With 3 workers, average product is 150.

Therefore, total product with 3 workers is 150*3 i.e. 450

Marginal Product is addition to the total product when one more unit of worker is employed. We know that marginal product of 4^th worker is 75. Therefore, total product with 4 workers is 450+75 i.e. 525

(ii) The minimum efficient scale (MES) of production is the lowest point on a total cost curve at which a company can produce its product at a competitive price. At this point, the firm achieves the economies of scale which is necessary to compete efficiently in the market.

(iii)

Case I

F(L,K) = Q = 300K + 25L

Suppose we increase inputs by λ times

F(λL, λK) = 300λK +25λL

F(λL, λK) = λ(300K +25L)

F(λL, λK) = λ(Q)

From above we can observe that when inputs are increased by λ times output increases by λ times. Thus, production function exhibits constant returns to scale.

Case II

F(L,K) = Q = 50K^0.3L^0.5

Suppose we increase inputs by λ time

F(λ L, λ K) = 50 (λ K)^0.3 (λ L)^0.5

F(λ L, λ K) = (λ^0.3) (λ^0.5) [50 K^0.3L^0.5]

F(λ L, λ K) = (λ^0.3+0.5) [50 K^0.3L^0.5]

F(λ L, λ K) = (λ^0.8) [50 K^0.3L^0.5]

F(λ L, λ K) = (λ^0.8) Q

From above we can observe that when inputs are increased by λ times, output increases by λ^0.8 times. Since increase in output is less than increase in inputs, this production function exhibits decreasing returns to scale.