Question

PROBLEM SET 7

Question 1

Erika, Ayami and Alison are partners in a fast growing food distribution business in Courtenay. To maximize their profit in the long-run by using the right mix of inputs, what should be their decision when labour or capital varies? (2 lines)

2 Marks

Question 2

You recently replace Antonia, the manager of Division 3, despite Antonia’s strong external sales record. Division 3 produces frozen drinks. Frozen drinks are relatively simple to make. Ignoring the ingredients, it requires only labour and a blender. As you begin reviewing the company’s production information, you learn that labour is paid $8 per hour and the last worker produced 100 drinks per hour. The company rents blenders for $15 per hour and the marginal product of capital is 120 drinks per hour. What do you think Antonia could have done to keep his job? Explain (3 lines)

2 Marks

Question 3

A firm has two plants, one in the United States and one in Canada, and it cannot change the size of the plants or the amount of capital equipment. The wage in Canada is $5. The wage in the U.S. is $20. Given current employment, the marginal product of the last worker in Canada is 100, and the marginal product of the last worker in the U.S. is 500.

a. Is the firm maximizing output relative to its labor cost? Show how you know. (2 lines)

b. If it is not, what should the firm do? (2 lines)

3 Marks

Question 4

Explain why one of diseconomies of scale and diminishing marginal product of the variable factors is a short-run concept and the other a long run concept.

3 Marks

Answer 1

Question 1

To maximize their profit in the long-run by using the right mix of inputs, they must follow the equimarginal principle where ratio of marginal product of an input with its price should be equal across all inputs. This implies

MPL/PL = MPK/PK...... for all factors

Question 2

Labour is paid $8 per hour and the last worker produced 100 drinks per hour. Hence MPL/PL = 100/8 = 12.5. The company rents blenders for $15 per hour and the marginal product of capital is 120 drinks per hour. Hence 120/15 = 8. Since equimarginal principle is not followed current input mix is not optimal. Here MPL/PL > MPK/PK. This shows that labor is more productive. Hence, Antonia could have hired more labor and use less capital to keep his job

Question 3

The wage in Canada is $5. The wage in the U.S. is $20. Given current employment, the marginal product of the last worker in Canada is 100, and the marginal product of the last worker in the U.S. is 500.

a. The firm is not maximizing output relative to its labor cost. In Canada, MPL/PL = 100/5 = 20 and in the US, MPL/PL = 500/20 = 25. Since the two ratios are not same equimarginal principle is not follwed and too many workers are employed in Canada

b. Hence it can hire more labor in the US and reduce workers in Canada because Labor is more productive in the US than the labor in Canada.

Question 4

Diseconomies of scale is a long run concept because it is measured along the long run average total cost while diminishing marginal product of the variable factors is a short-run concept because capital is assumed fixed in this case.