Solutions to Problems - Pearson Education



Solutions to Problems

Chapter 14

1a. The wage rate is $6 an hour. The wage rate adjusts to make the quantity of labour demanded equal to the quantity supplied (see figure 1).

1b. The number of pickers hired is 400 a day. At a wage rate of $6 an hour, 400 pickers a day are hired (see figure 1).

1c. The income received is $2,400 an hour.

Income = wage rate multiplied by the number of pickers

= $6x400

= $2,400 an hour

Figure 1 Figure 2

3a. Marginal product of labour is the increase in total product that results from hiring one additional student. The marginal product of labour schedule for Wanda’s fish shop is shown in table 1 and the marginal product of labour curve (MP) derived from this schedule is shown in figure 3.

figure 3

3b. Marginal revenue product of labour is the increase in total revenue that results from hiring one additional student. The marginal revenue product schedule for Wanda’s fish shop is shown in table 1 and the marginal revenue product curve (MRP) derived from this schedule is shown in figure 3.

3c. Wanda’s demand for labour curve is the same as the downward sloping section of the marginal revenue product curve MRP in figure 3.

3d. Wanda hires 7 students.

Wanda hires the number of students that makes the marginal revenue product equals to the wage rate of $7.50 an hour. When Wanda increases the number of students from 6 to 7, marginal product is 15 kilograms of fish an hour, which Wanda sells for 50 cents a kilogram. Marginal revenue product is $7.50—the same as the wage rate (see table 1).

|Table 1 ( Problems 3&7 |

|Fish sells for $0.50 per kilogram |

|Number of |Q |AP |MP |ARP |MRP |

|students |(Kgs per hour) |(Q/L) |(dQ/dL) |$(PxAP) |$(PxMP) |

|1 |20 |20.00 | |10.00 | |

|2 |50 |25.00 |30 |12.50 |15.00 |

|3 |90 |30.00 |40 |15.00 |20.00 |

|4 |120 |30.00 |30 |15.00 |15.00 |

|5 |145 |29.00 |25 |14.50 |12.50 |

|6 |165 |27.50 |20 |13.75 |10.00 |

|7 |180 |25.71 |15 |12.86 |7.50 |

|8 |190 |23.75 |10 |11.88 |5.00 |

5a. Marginal product does not change (see table 3).

5b. Marginal revenue product decreases.

The new marginal revenue product schedule for Wanda’s fish shop is shown in table 3 and the marginal revenue product curve (MRP/) derived from this schedule is shown in figure 3.

5c. Wanda's demand for labour decreases, and her demand for labour curve shifts leftward from MRP to MRP/ in figure 3. Wanda is willing to pay the students their marginal revenue product, and the fall in the price of fish has lowered their marginal revenue product.

5d. Wanda will employ 5 students.

At the wage rate of $7.50, the number of students Wanda hires decreases as the demand for labour curve shifts leftward. The fifth student adds $8.33 to revenue and will be employed. The sixth student adds $6.67 to revenue, less than his wage and will not be employed (see table 3).

|Table 3 ( Problem 5 |

|The wage rate is $7.50 Fish sells for $0.50 Fish sells for $0.3333 |

|per kilogram per kilogram |

|Number of |Q |MP |MRP |MP |MRP |

|students |(Kgs per hour) |(dQ/dL) |$(PxMP) |(dQ/dL) |$(PxMP) |

|1 |20 | | | | |

|2 |50 |30 |15.00 |30 |10.00 |

|3 |90 |40 |20.00 |40 |13.33 |

|4 |120 |30 |15.00 |30 |10.00 |

|5 |145 |25 |12.50 |25 |8.33 |

|6 |165 |20 |10.00 |20 |6.67 |

|7 |180 |15 |7.50 |15 |5.00 |

|8 |190 |10 |5.00 |10 |3.33 |

7a. Marginal revenue product does not change because there has been no change in the price of fish or the marginal product of labour (see table 1).

7b. Wanda's demand for labour remains the same because marginal revenue product has not changed.

7c. Wanda will hire fewer students. At the wage rate of $10 an hour, Wanda hires the number of students that makes marginal revenue product equal to $10 an hour. Wanda now hires 6 students—down from 7. The marginal product that results when Wanda hires the sixth student is 20 kilograms of fish an hour, and Wanda sells this fish for 50 cents a kilogram. Marginal revenue product of the sixth student is $10 an hour (see table 1).

9. Wanda maximizes her profit when marginal revenue product equals the wage rate and when marginal revenue equals marginal cost.

When the wage rate is $7.50 an hour, Wanda hires 7 students.

Marginal revenue product = marginal product x price

= 15 x $0.50

= $7.50 an hour = wage rate.

Marginal revenue = price

= 50 cents.

Marginal cost = Wage rate ( marginal product

= $7.50 ( 15

= 50 cents = marginal revenue.

So when Wanda hires 7 students, marginal revenue equals marginal cost and profit is maximized (see table 5.

|Table 5 ( Problem 9 |

|Fish sells for $0.50 per kilogram Wage rate is $7.50 per hour |

|L |Q |MR |TVC |MC |MRP |

|(students) |(Kgs per hour) |(price) |(LxW) |(dTVC/dQ) |$(PxMP) |

|1 |20 | |7.50 | | |

|2 |50 |0.50 |15.00 |0.25 |15.00 |

|3 |90 |0.50 |22.50 |0.19 |20.00 |

|4 |120 |0.50 |30.00 |0.25 |15.00 |

|5 |145 |0.50 |37.50 |0.30 |12.50 |

|6 |165 |0.50 |45.00 |0.38 |10.00 |

|7 |180 |0.50 |52.50 |0.50 |7.50 |

|8 |190 |0.50 |60.00 |0.75 |5.00 |

11. Venus installs two production lines.

The cost of the first production line is $1 million. The net present value is $1,097,052 so Venus buys the production line.

The cost of the second production line is $1 million. The net present value is $1,041,270 so Venus buys the production line.

The cost of the third production line is $1 million. The net present value is $985,488 so Venus does not buy the production line.

|Table 7 ( Problem 11 |

|Interest rate 5% |

| |Net Present |Cost |Present Value of |Present Value of |Present Value of |

| |Value | |marginal revenue product|year 1 income |year 2 income |

|Plant 1 |97,052 |1,000,000 |1,097,052 |590,000/1.05 = 561,905 |590,000/1.052 = 535,147 |

|Plant 2 |41,270 |1,000,000 |1,041,270 |560,000/1.05 = 533,333 |560,000/1.052 = 507,936 |

|Plant 3 |-14,512 |1,000,000 |985,488 |530,000/1.05 = 504,762 |530,000/1.052 =480,725 |

13. To answer this problem, we need to know the interest rate and the price that Greg expects next year. If he expects the price to rise by a bigger percentage than the interest rate, he pumps none and waits for the higher price. If he expects the price to rise by a smaller percentage than the interest rate, he pumps it all now. If he expects the price to rise by a percentage equal to the interest rate, he doesn't mind how much he pumps.

14. Income of $2,400 a day is divided between opportunity cost and economic rent. Economic rent is the area above the supply curve below the wage rate (see figure 1).

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download