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In the below figure, a consumer is initially in equilibrium at point C

Subject: Economics    / General Economics
Question

1. In the below figure, a consumer is initially in equilibrium at point C. The consumer’s income is \$300, and the budget line through point C is given by \$300 = \$100X + \$150Y. When the consumer is given a \$200 gift certificate that is good only at store X, she moves to a new equilibrium at point D.

Created with Raphaël 2.1.0

Product Y

Product X

A

B

C

D

E

F

I

2

I

1

a. Determine the prices of goods X and Y.

Price of X: \$

Price of Y: \$

b. How many units of product Y could be purchased at point A?

c. How many units of product X could be purchased at point E?

d. How many units of product X could be purchased at point B?

e. How many units of product X could be purchased at point F?

f. Based on this consumer’s preferences, rank bundles A, B, C, and D in order from most preferred to least preferred.

(Click to select)A, B, C, DD, B, C, AD, C, A, BC, A, B, D

g. Is product X a normal or an inferior good?

(Click to select)NormalInferior

2.A consumer’s budget set for two goods (X and Y) is 1,000 ? 5X + 10Y.

a. The budget set is illustrated below. What are the values of A and B?

Good Y

Good X

A

B

A =

B =

b. Does the budget set change if the prices of both goods double and the consumer’s income also doubles?

Yes, it shifts in toward the origin.

Yes, it rotates clockwise.

Yes, it shifts out from the origin.

No, it does not change.

c. Given the equation for the budget set, what are the prices of the two goods?

Good X: \$

Good Y: \$

What is the consumer’s income?

3. A worker views leisure and income as “goods” and has an opportunity to work at an hourly wage of \$10 per hour.

a. The worker’s opportunity set in a given 24-hour period is illustrated below. What are the values of A and B?

Income

Leisure

A

B

A =B = b. Suppose the worker is always willing to give up \$14 dollars of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?

B =

b. Suppose the worker is always willing to give up \$14 dollars of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution?

Yes or No?

How many hours per day will she choose to work?

4. Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with workers’ compensation and has decided to cut the wages of its two employees (Albert and Sid) from \$23 per hour to \$20 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Albert and Sid’s opportunity set is presented below:

0

5

10

15

20

25

30

Albert and Sid’s Opportunity Set

Income

Leisure Hours

A

What is the value of A when the wage is \$23?

What is the value of A when the wage is \$20?

At the wage of \$23 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and equivalently supply 12 hours of labor). After wages were cut to \$20, Albert consumes 10 hours of leisure and Sid consumes 15 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of \$20 per hour:

Albert’s supply of labor =

Sid’s supply of labor =

How can you explain the seemingly contradictory result that the workers supply a different number of labor hours?

Albert’s substitution effect dominates his income effect when the wage declines to \$20, and vice versa for Sid.

Albert’s income effect dominates his substitution effect when the wage declines to \$20, and vice versa for Sid.

Albert has no substitution effect, and Sid has no income effect when the wage declines to \$20.

Albert has no income effect, and Sid has no substitution effect when the wage declines to \$20.

5. A large Coca Cola vendor recently hired some economic analysts to assess the effect of a price increase in its 16 ounce bottles from \$1.00 to \$1.50. The analysts determined that, on average, the vendor’s customers spend about \$17.00 on soda (Coke and all other brands) each week, and the average price for other 16-ounce soda bottles is \$1.00. The analysts also utilized some focus groups to determine the preferences of the vendor’s customers. They used this analysis to build the following graph:

Created with Raphaël 2.1.0

Bottles of Other Soda

Bottles of Coke

X

1

X

0

Budget Line beforePrice Increase

Budget Line afterPrice Increase

Suppose X0 = 9 and X1 = 6. Should the vendor expect to sell 6, more than 6, or less than 6 bottles of Coke after raising the price to \$1.50 if Coke is a normal good?

Choose One:

The vendor should expect to sell 6 bottles of Coke.

The vendor should expect to sell more than 6 bottles of Coke.

The vendor should expect to sell less than 6 bottles of Coke.

6. When trying to assess differences in her customers, Claire – the owner of Claire’s Rose Boutique – noticed a difference in the typical demand of her female versus her male customers. In particular, she found her female customers to be more price sensitive in general. After conducting some sales analysis, she determined that her female customers have the following demand curve for roses: QF = 24 – 2.50*P. Here, QF is the quantity of roses demanded by a female customer, and P is the price charged per rose. She determined that her male customers have the following demand curve for roses: QM = 28 – 1.50*P. Here, QM is the quantity of roses demanded by a male customer. If two unaffiliated customers walk into her boutique, one male and one female, determine the demand curve for these two customers combined (i.e., what is their aggregate demand?). (Note: QT represents total, or aggregate, demand. Solve for the demand curve for prices less than \$12.)??QT = – P

7. An economist estimated that the cost function of a single-product firm is:

C(Q) = 110 + 35Q + 30Q2 + 5Q3.

Based on this information, determine the following:

a. The fixed cost of producing 10 units of output.

\$

b. The variable cost of producing 10 units of output.

\$

c. The total cost of producing 10 units of output.

\$

d. The average fixed cost of producing 10 units of output.

\$

e. The average variable cost of producing 10 units of output.

\$

f. The average total cost of producing 10 units of output.

\$

g. The marginal cost when Q = 10.

\$

8. A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is \$15 per hour and capital is rented at \$8 per hour. If the marginal product of labor is 45 units of output per hour and the marginal product of capital is 65 units of output per hour, should the firm increase, decrease, or leave unchanged the amount of capital used in its production process?

Choose One:

The firm should leave capital unchanged.

The firm should increase capital.

The firm should decrease capital.

9. A firm produces output according to a production function:

Q = F(K,L) = min {9K,3L}.

a. How much output is produced when K = 2 and L = 3?

b. If the wage rate is \$60 per hour and the rental rate on capital is \$40 per hour, what is the cost-minimizing input mix for producing 9 units of output?

Capital:

Labor:

c. How does your answer to part b change if the wage rate decreases to \$40 per hour but the rental rate on capital remains at \$20 per hour?

Choose One:

It does not change.

Capital and labor increase.

Capital increases and labor decreases.

Capital decreases and labor increases.

10. You were recently hired to replace the manager of the Roller Division at a major conveyor-manufacturing firm, despite the manager’s strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company’s production information, you learn that labor is paid \$8 per hour and the last worker hired produced 90 rollers per hour. The company rents roller cutters and crimping machines for \$13 per hour, and the marginal product of capital is 110 rollers per hour.

Should you change the mix of capital and labor, and if so, how should it change?

Choose One:

You should increase capital and decrease labor.

You should increase labor and decrease capital.

You should not change the mix of capital and labor.

11. The World of Videos operates a retail store that rents movie videos. For each of the last 10 years, World of Videos has consistently earned profits exceeding \$37,000 per year. The store is located on prime real estate in a college town. World of Videos pays \$2,100 per month in rent for its building, but it uses only 50 percent of the square footage rented for video rental purposes. The other portion of rented space is essentially vacant. Noticing that World of Videos only occupies a portion of the building, a real estate agent told the owner of World of Videos that she could add \$1,650 per month to her firm’s profits by renting out the unused portion of the store. While the prospect of adding an additional \$1,650 to World of Videos’s bottom line was enticing, the owner was also contemplating using the additional space to rent video games. What is the opportunity cost of using the unused portion of the building for video game rentals?

\$

12. According to The Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labor and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.16 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,740. In the study of its production process and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.8 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is ¥1,400,000. Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output.

Instruction: Round your answer for marginal productivity of labor to 4 decimal places.

Rental rate of capital: ¥

Marginal productivity of labor:

To minimize costs Mitsubishi should hire capital and labor until the marginal rate of technical substitution reaches what proportion?