Question

In: Economics

1. Suppose tin mine’s workers can dig up two tons of tin ore per hour and...

1. Suppose tin mine’s workers can dig up two tons of tin ore per hour and tin ore sells for $20 per ton. Also assume that the tin mine is the only hirer of miners and faces the following labor supply function:

I =30w

where I is the number of workers per hour and w the wage rate per hour and that the firm’s hiring decisions affect wages.

Calculate the following:

a. the marginal revenue product per hour of the tin mining firm;

b. the number of workers per hour the firm would hire

c. the wage rate (in $/hour)

d. the number of workers that would be hired if the firm is forced by market competition to pay according to the marginal revenue product regardless of the number of miners employed.

e. Explain how an increase in the real wage rate could affect the demand for leisure and hence labor supply.

Solutions

Expert Solution

1) MP of each worker = 2

Price of output = 20

Monopsony outcome, ( as there is a single employer )

A) MRPL = MR * MP

= 20*2= 40

B) at eqm, MRPL = MFC ( marginal factor cost )

MFC has twice the slope of that of Labor supply curve

So Labor supply curve , w = I/30

MFC = I/15

So at eqm , 40 = I/15

I* = 600

c) now wage rate is found from the Labor supply curve.

w* = 600/30 = 20 $ / hour

d) in perfect competition,

Wage = MRPL

W`= 40

e)now at w = 40, I = 30*40 = 1200

So as wage rises, then demand for leisure falls & supply of Labor rises.

Rahul Sunny answered 2 years ago
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