Frequent Exam Questions with Answers
Utility in Bundles: The Equimarginal Principle and Indifference Analysis
Chapter 8 ― Question 4
Below you find the utility a consumer derives from buying three commodities A, B and C.
| Product | A | B | C |
| Quantity | 2 | 3 | 4 |
| Price per unit | $5 | $7 | $9 |
| Utility derived from the last unit | 10 utils | 10 utils | 10 utils |
The consumer
- has made a rational decision because all three products yield the same marginal utility
- should decrease purchases of C
- should decrease purchases of A and B and increase purchases of C
- should increase purchases of A
*D. Answer A is a trap. The marginal utility alone is not relevant. What counts is MU/P. This is highest for Commodity A. Remember the rule: You should increase consumption of the commodity whose MU/P has the highest value.
Chapter 8 ― Question 7
A consumer buys a bundle of two goods, A and B. MU/P for A is 40/1. The marginal utility of B is 20. The price of B must therefore be
- 5
- 0.5
- 2
- none of the above
*B. The ratio 40/1 for A is the same as 20/0.5 for B.
Chapter 8 ― Question 8
A consumer buys a bundle with two goods, X and Y. MU/P for X is 4, MU/P for Y is 3. What should the consumer do to optimise his decision with the same amount of money?
- increase X
- increase Y
- increase Y and lower X
- increase X and lower Y
*D. Always increase consumption of the commodity whose MU/P has a higher value.
Answer A is not correct because, if the amount of money remains the same, the consumer must lower Y to increase X.
Chapter 8 ― Question 16
Your optimal buying decision is to buy 20 units of A at $1 and 5 units of B. The last A gave you 10 units of utility. The last unit of B gave you 20 units of utility. The price of B is
- $0.50
- $0.25
- $4.00
- $2.00
*D. MU/P for A is 10/1. MU/P for B is 20/? The price of B must therefore be $2.00.
The trap in this question is that the total numbers of units are indicated. They are, however, irrelevant to the answer.
Chapter 9 ― Question 10
Using our wine-water example, write down the equations which a consumer uses to make an optimal choice between water and wine
1) when he applies the equimarginal principle for bundles 2) when he applies indifference analysis
| *1) | Marginal utility of water Price of water |
= |
Marginal utility of wine Price of wine |
| *2) | Amount of water sacrificed Amount of wine gained |
= |
Price of wine gained Price of water sacrificed |
The clue to the answer is that the equimarginal principle uses market prices while indifference analysis uses barter prices.
Chapter 9 ― Question 11
A consumer's budget for commodity X and commodity Y is $100. X costs $10 per unit, Y $5 per unit.
1) Draw the budget line on a diagram.
2) The consumer wants to spend half of his budget on each commodity. Label this point on the budget line.
3) What is the marginal rate of substitution between X and Y at this point?
*1) Here is the schedule for the budget line:
X 0 1 2 3 4 5 6 7 8 9 10
| *3) | Change in Y | = |
2 |
= |
2. |
| Change in X | 1 |
Chapter 9 ― Question 15
Your utility function for commodities x and y is u(x,y) = 8x + 4y. You buy 10 units of x and 4 units of y. You now lower your purchases of x to 8. How many units of y must you buy to get the same utility?
- 8 units of y
- 4 units of y
- 12 units of y
- None of the above.
*A. You used to have 96 utils. You then changed your mind and had 64x only. To receive the initial 96 utils, you must buy 8 units of y, which yield 32 utils. (I am sorry for the utils. I have written often enough in the book that they do not exist. But you are asked such questions in exams.)
Chapter 9 ― Question 17
You are offered a job. The pay is $10 per hour. You can choose the number of hours. The maximum you are able to work is 50 hours. Your utility function for leisure and money to spend on consumption is U(C,L) = CL.
1) Write down your budget constraint for leisure and consumption. This gives you your options in terms of the allocation of time. (Consider only options with a difference of 5 hours, otherwise the list becomes too long.)
2) Calculate the utility each bundle yields. This gives you your options in terms of utility.
3) Find the optimal bundle of leisure and consumption.
*1) Here is your budget constraint:
| Option | Leisure | Work |
| A | 0 | 50 |
| B | 5 | 45 |
| C | 10 | 40 |
| D | 15 | 35 |
| E | 20 | 30 |
| F | 25 | 25 |
| G | 30 | 20 |
| H | 35 | 15 |
| I | 40 | 10 |
| J | 45 | 5 |
| K | 50 | 0 |
*2) The calculation of utility with the help of your utility function shows you your options in terms of utility.
| Option | Leisure | Consumption | Utility |
| A | 0 | 500 | 0 |
| B | 5 | 450 | 2250 |
| C | 10 | 400 | 4000 |
| D | 15 | 350 | 5250 |
| E | 20 | 300 | 6000 |
| F | 25 | 250 | 6250 |
| G | 30 | 200 | 6000 |
| H | 35 | 150 | 5250 |
| I | 40 | 100 | 4000 |
| J | 45 | 5 | 2250 |
| K | 50 | 0 |
0 |
*3). Optimal bundle: F
Please note that such questions are very, very frequent. The utility function for leisure and money is an instrument to prove that unemployment is voluntary.
Chapter 9 ― Question 18
Explain why two indifference curves cannot intersect.
* An intersection would violate the more-is-better rule. An intersection would imply that you switch from a higher indifference curve to a lower one or vice versa. The lower one has fewer units of both goods everywhere.
If you like, print this page for offline comparison or studying.