Question

1. The data in the table represent a production function in which labour is a variable

Labour (hours) Total physical product
1 15
2 35
3 60
4 90
5 120
6 144
7 158
8 160
9 60
10 158
a. Calculate the marginal products and average products at each level of labour. [6 marks]
b. Sketch on the same axes the graph of marginal, average and total products and label the three stages of production in the short run. [4 marks]
c. Explain the characteristics of each of the above stages of production. Which stage should a rational produce operate in and why? [8 marks]
2. Use a well labeled diagram to distinguish between income and substitution effect for a normal good after decrease in price of commodity X ceteris paribus [8 marks]
3. Clearly explain the difference between an isoquant and marginal rate of substitution. [4 marks]

Answer 1

a. The marginal product (MP) can be calculated as the change in total physical product (TPP) for a one-unit increase in labor input. The average product (AP) can be calculated as the total physical product divided by the labor input. Using the table, we can calculate:

Labor (hours) TPP MP AP

1 15 15 15

2 35 20 17.5

3 60 25 20

4 90 30 22.5

5 120 30 24

6 144 24 24

7 158 14 22.57

8 160 2 20

9 60 -100 6.67

10 158 98 15.8

b. The graph of marginal, average, and total product can be sketched as follows:

[Graph not included]

The three stages of production are labeled as follows:

Stage I: Increasing marginal returns (region between Labor input 1 and 6)

Stage II: Decreasing marginal returns (region between Labor input 6 and 8)

Stage III: Negative marginal returns (region after Labor input 8)

c. In stage I, the marginal product of labor is increasing, and the average product of labor is also increasing, but at a decreasing rate. In stage II, the marginal product of labor is decreasing, and the average product of labor is still increasing but at a decreasing rate. In stage III, the marginal product of labor is negative, and the average product of labor is decreasing. A rational producer should operate in stage II, where the marginal product of labor is still positive and the average product of labor is still increasing, but at a decreasing rate.

2. The income and substitution effects can be shown using an indifference curve diagram. When the price of commodity X decreases, the budget constraint shifts outward, increasing the consumer's purchasing power. The substitution effect shows the change in quantity demanded of the good as the consumer substitutes it for other goods. The income effect shows the change in quantity demanded due to the change in purchasing power. The total effect is the combination of the substitution and income effects.

[Diagram not included]

3. An isoquant is a curve that shows the combinations of inputs that produce the same level of output. The marginal rate of substitution (MRS) is the amount of one input that must be given up in order to obtain an additional unit of another input while keeping output constant. The MRS is the slope of the isoquant. In other words, the MRS measures the rate at which a firm can substitute one input for another while keeping the same level of output.

Step-by-step explanation: