Question

12. If the labor supply curve faced by a monopsony is given by -800 +50W, then the correct marginal expenditure curve will be: O w = 16-004 , =-800 + 25 W =-800 + 100w. ︵ w 16-0.021.

Answer 1

Solution:

NOTE: correct option is missing, either verify the question again.

l = -800 + 50W

So, W = (l/50) +(800/50)

W = 0.02l + 16

We shall work for the correct answer both, mathematically and intuitively or logically. Marginal expenditure is simply the extra expenditure a firm has to incur to hire an additional labor.

First, going with logics, under perfect competition, this is simply the wage rate, as an additional labor receives the prevailing wage rate, and the already employed labor earn the same wage rate. (MEC = W)

Under monopsony, however, an additional labor receives a higher wage rate. And thus, all the already employed labor also earn that wage differential. Hence, the additional cost incurred is not just the wage rate, but also that wage differential to be paid to entire labor. Hence, marginal expenditure curve has the following expression:

MEC = W + (dW/dl)*l; where W is wage rate, l is labor quantity.

Note that labor supply curve simply tells at what wage, w, how many labors are willing to supply their service, l.

We can note two points from all this (taking wage, w on vertical axis and labor, l on horizontal axis)

1) Wage, W and labor, l are positively related (that is as wage rate increases, labor supply increases).

2) As an additional labor is hired, additional expenditure increases by more than the wage (due to the differential). Thus, marginal expenditure curve lies above the labor supply curve. Also, for the first unit of labor, marginal expenditure will be wage itself (since, that is the first unit) so vertical intercept for MEC and labor supply curve remains same. And since for every l, MEC lies above Labor supply curve, MEC is steeper than labor supply, or MEC has a higher slope.

So MEC equation: W = 16 + m*l , m > 0.02

Mathematically, using the equation: MEC = W + (dW/dl)*l

We already know since W = 16 + 0.02*l

dW/dl = 0.02

So, MEC = (16 + 0.02*l) + (0.02)*l

W = 16 + 0.04*l

Thus, m = 0.04

This is our required marginal expenditure curve function:

W = 16 + 0.04*l

Or l = -400 + 25*W