Economics 101

Fall 2001

Answers to Practice Questions 9

Question 1: 

Add a third column to the table to calculate the marginal revenue product as follows:


 
# of pickers
Revenue from pumpkin sales
Marginal Revenue Product (MRP)
1
$30
2
$48
$18
3
$62
$14
4
$72
$10
5
$80
$8
6
$84
$4

Consider the 4th worker: this worker costs the farmer $9 per day, but he

adds to the revenues $10 per day. Thus, the farmer should hire the fourth
worker because in doing so he can increase his profits. Now consider the
5th worker: this worker costs the farmer $9 per day too, but he adds to
the revenues $8 per day. If the farmer hires this 5th worker, he'll be
making a loss of $1 per day for hiring this worker, i.e. it reduces the
profits of the farmer. Therefore, the farmer should hire 4 workers in
order to maximize his profits.
 
 

Question 2:

The profit maximization condition for firm A requires MFC = MRP. By definition, MRP = MR.MP and in a perfectly competitive market P = MR. Therefore, MRP for firm A is given by: MRP = (6)(8) = $48 and from the profit maximization condition, we get MFC = $48. Since the labor market is perfectly competitive, MFC for firm B is also $48. Thus, for firm B: MFC = $48 = MRP = MR.MP = MR.12. Solving for MR, we get MR = $4 = P (since firm B also operates in a perfectly competitive market, P = MR).

Question 3: 

First, consider the market for shoes: we can find the market equilibrium using the demand and the supply equations. The equilibrium price in the market is $50 and the equilibrium quantity in the market is 50 shoes. Since East Ten is a perfectly competitive firm, it will take this market price as given and note that P = MR =$50 for East Ten. The firm hires labor in a perfectly competitive labor market, and this implies W = MFC. The perfectly competitive labor market will be in equilibrium when labor demand equals labor supply, and we can calculate the labor market equilibrium using the labor demand and labor supply equations: equilibrium wage rate is $400 per week and equilibrium quantity of workers hired is 200. Also, the profit maximization condition is MFC = MR.MP. Thus, 400 = 50(30 – L) and L = 22.

Question 4: 

We need to find the market demand curve. Note that the market demand curve will have a kink since for wages higher than 100 only the automobile manufacturer is in the market. Recall that the market demand curve is the horizontal summation of the individual demand curves. Thus, for wages between 0 and 100, we have the following demand equation: L = 60 – (2/5) W, and for wages between 100 and 200, the demand equation is L = 40 – (1/5) W (note that this is the upper portion of the demand curve of the manufacturer). In order to find the equilibrium, use this demand curve with the supply equation given in the question: equilibrium wage is $50, and a total of 40 workers are hired. The catering firm hires 10 out of these 40 workers and the manufacturer hires the remaining 30.

Multiple Choice Questions:

  1. (d) Since P = MR in the perfectly competitive output market and W = MFC in the perfectly competitive labor market, we can rewrite the profit maximization condition MFC = MRP as W = MP.P.
  2. (d) Using the condition above in question 1, the wage rate equals $20.
  3. (a) An increase in population will increase the number of people in the labor force.