The manager of All City Realtors wants to hire some real estate agents to specialize in selling housing unit acquired by the Resolution Trust Corporation (RTC) in its attempt to bail out the savings and loan industry. The commission paid by the RTC to the company to sell these homes is a flat rate of $2,000 per unit sold, rather than the customary commission that is based on the sale price of a home. The manager estimates the following marginal product schedule for real estate agents dealing in government-owned housing:
Number of real Marginal product Marginal
Estate agents (number of additional units sold per year) revenue product
1 20 _______
2 17 _______
3 15 _______
4 12 _______
5 8 _______
6 4 _______
a) Construct the marginal revenue product schedule by filling in the blanks in the table.
b) If the manager of All City Realtors must pay a wage rate of $32,000 per year to get agents who will specialize in selling RTC housing, how many agents should the manager hire? Why?
c) If the wage rate falls to $18,000 per year, how many agents should the manager hire?
d) Suppose the RTC raises its commission to $3,000 per unit sold. Now what is the marginal revenue product for each real estate agent employed?
e) Now that the RTC is paying $3,000 per unit sold, how many agents should the manager hire if the wage rate is $30,000?
a) To fill in the blanks in the table, we need to find the difference between the number of additional units sold per year when each additional real estate agent is hired:
Number of real Marginal product Marginal revenue product
Estate agents (units sold per year)
1 20 $40,000
2 17 $34,000
3 15 $30,000
4 12 $24,000
5 8 $16,000
6 4 $8,000
b) To determine how many agents the manager should hire, we need to compare the marginal revenue product to the wage rate. In this case, the wage rate is $32,000. Looking at the table, we can see that hiring 3 agents would generate a total of $90,000 in revenue ($30,000 * 3). Since this is greater than the wage rate, the manager should hire 3 agents.
c) If the wage rate falls to $18,000 per year, we can calculate the total revenue generated by each additional agent:
Number of real Marginal product Marginal revenue product
Estate agents (units sold per year)
1 20 $40,000
2 17 $34,000
3 15 $30,000
4 12 $24,000
5 8 $16,000
6 4 $8,000
Comparing the marginal revenue product to the wage rate, we can see that hiring 4 agents would generate a total revenue of $96,000 ($24,000 * 4). Since this is greater than the wage rate, the manager should hire 4 agents.
d) If the RTC raises its commission to $3,000 per unit sold, the marginal revenue product for each real estate agent employed would be:
Number of real Marginal product Marginal revenue product
Estate agents (units sold per year)
1 20 $60,000
2 17 $51,000
3 15 $45,000
4 12 $36,000
5 8 $24,000
6 4 $12,000
e) Now that the RTC is paying $3,000 per unit sold, and the wage rate is $30,000, we can compare the marginal revenue product to the wage rate:
Number of real Marginal product Marginal revenue product
Estate agents (units sold per year)
1 20 $60,000
2 17 $51,000
3 15 $45,000
4 12 $36,000
5 8 $24,000
6 4 $12,000
Since hiring 2 agents would generate a total revenue of $102,000 ($51,000 * 2), which is greater than the wage rate, the manager should hire 2 agents.
To construct the marginal revenue product schedule, we need to calculate the marginal revenue product for each number of real estate agents.
a) Marginal revenue product can be calculated by multiplying the marginal product by the commission paid per unit sold.
Number of real Marginal product Marginal
Estate agents (number of additional units sold per year) revenue product
1 20 $2,000 * 20 = $40,000
2 17 $2,000 * 17 = $34,000
3 15 $2,000 * 15 = $30,000
4 12 $2,000 * 12 = $24,000
5 8 $2,000 * 8 = $16,000
6 4 $2,000 * 4 = $8,000
b) To determine the number of agents the manager should hire, we need to compare the marginal revenue product with the wage rate. The manager should continue to hire agents as long as the marginal revenue product is greater than or equal to the wage rate.
In this case, the wage rate is $32,000. Looking at the marginal revenue product schedule, the manager should hire up to 3 agents because the marginal revenue product is greater than the wage rate for the first 3 agents. Hiring more than 3 agents would result in a marginal revenue product lower than the wage rate, leading to a loss for the company.
c) If the wage rate falls to $18,000, we again compare the wage rate with the marginal revenue product. Looking at the marginal revenue product schedule, the manager should hire up to 5 agents because the marginal revenue product is greater than the wage rate for the first 5 agents. Hiring 6 agents would result in a marginal revenue product lower than the wage rate, leading to a loss for the company.
d) If the RTC raises its commission to $3,000 per unit sold, we need to recalculate the marginal revenue product for each real estate agent employed.
Number of real Marginal product Marginal
Estate agents (number of additional units sold per year) revenue product
1 20 $3,000 * 20 = $60,000
2 17 $3,000 * 17 = $51,000
3 15 $3,000 * 15 = $45,000
4 12 $3,000 * 12 = $36,000
5 8 $3,000 * 8 = $24,000
6 4 $3,000 * 4 = $12,000
e) Now that the RTC is paying $3,000 per unit sold, and the wage rate is $30,000, we compare the wage rate with the marginal revenue product. Looking at the revised marginal revenue product schedule, the manager should hire up to 4 agents because the marginal revenue product is greater than the wage rate for the first 4 agents. Hiring 5 or 6 agents would result in a marginal revenue product lower than the wage rate, leading to a loss for the company.
a) To construct the marginal revenue product schedule, we need to calculate the marginal revenue product for each level of output.
The marginal revenue product is calculated by multiplying the marginal product with the price of the output. In this case, the price is the flat rate commission of $2,000 per unit sold.
Number of real Marginal product Marginal revenue
Estate agents (additional units product
sold per year)
1 20 $2,000 * 20 = $40,000
2 17 $2,000 * 17 = $34,000
3 15 $2,000 * 15 = $30,000
4 12 $2,000 * 12 = $24,000
5 8 $2,000 * 8 = $16,000
6 4 $2,000 * 4 = $8,000
b) To determine how many agents the manager should hire at a wage rate of $32,000 per year, we need to compare the wage rate with the marginal revenue product.
The manager should hire agents as long as the wage rate is less than or equal to the marginal revenue product. From the table, we can see that the marginal revenue product is highest for the first agent ($40,000) and decreases as more agents are hired.
Since the wage rate is $32,000 and is less than the marginal revenue product of the first agent, it would be profitable for the manager to hire 1 real estate agent.
c) If the wage rate falls to $18,000 per year, we follow the same logic as in part b.
The manager should hire agents as long as the wage rate is less than or equal to the marginal revenue product. From the table, we can see that the marginal revenue product is highest for the first agent ($40,000), which is still greater than the wage rate of $18,000.
Therefore, the manager should still hire 1 real estate agent.
d) If the RTC raises its commission to $3,000 per unit sold, we need to update the marginal revenue product for each real estate agent employed.
Number of real Marginal product Marginal revenue
Estate agents (additional units product
sold per year)
1 20 $3,000 * 20 = $60,000
2 17 $3,000 * 17 = $51,000
3 15 $3,000 * 15 = $45,000
4 12 $3,000 * 12 = $36,000
5 8 $3,000 * 8 = $24,000
6 4 $3,000 * 4 = $12,000
e) Now that the RTC is paying $3,000 per unit sold and the wage rate is $30,000, we need to compare the wage rate with the updated marginal revenue product.
From the updated table, we can see that the marginal revenue product is highest for the first agent ($60,000).
Since the wage rate is $30,000 and less than the marginal revenue product of the first agent, it would be profitable for the manager to hire 1 real estate agent.