Answer to Question #89334 in Microeconomics for Areesha sajid

Question

A firm uses Labour (L) and capital (K) to product commodity (Y). The quantities of the inputs and outputs are shown in the table below.
L 0 1 2 3 4 5 6 7 8 9 10
K 90 90 90 90 90 90 90 90 90
Y 0 100 250 420 560 675 760 820
860 885 900

a) Calculate the average and marginal products of labour and plot them. What economic factors explain the shape of these curves? What is the range of output corresponding to the second stage of production?
b) Assuming that the wage rate is Rs.340/- and the rental rate on capital is Rs.0.5/-, calculate the short run average variable cost, marginal cost, average fixed cost, average total cost, total variable cost., total fixed cost and total cost. Plot all these curves.
c) Does the average variable cost cuts the marginal cost at the minimum point of the marginal cost? Why is this always the case? What is the relationship between the marginal cost and average variable cost in the second stage of production.

Answer 1

a) The average product of labour is: APL = Y/L and marginal products of labour

$$MPL = \Delta(Y) /\Delta(L)$$

In different stages of production the shape of these curves is different. In Stage II, marginal product is positive, but decreasing. 

b) The short run average variable cost is AVC = w = 340, marginal cost is

$$MC = \Delta{TC} /\Delta{Y}$$

Average fixed cost is AFC = r = 0.5, average total cost is ATC = AFC + AVC = 340.5, total variable cost is TVC = w×Y = 340Y, total fixed cost is TFC = r×Y = 0.5Y and total cost is TC = TFC + TVC = 340.5Y.

c) The average variable cost cuts the marginal cost at the minimum point of the marginal cost. Both marginal cost and average variable cost increase in the second stage of production.