Question

1. There are two goods, bread and butter. A person has spent all their income on bread and butter. The price of bread is $2 and the price of butter is $4. This person tells you that the last unit of bread he consumed increased his utility by 50 utils; the last unit of butter he consumed increased his utility by 80 utils. Has this person maximized his utility? If not, should he consume more bread and less butter OR less bread and more butter?

2. There are two goods, food and clothing. The price of food is $25 and the price of clothing is $100. A person has spent all their income on the two goods. The person has a marginal utility from food of 500 utils; the marginal utility of clothing is 3,000 utils. Has this person maximized his utility? If not, should he consume more food and less clothing OR less food and more clothing?

3. A person spends his entire income on the only two goods available. The last dollar spent on Good A increased his utility by 40 utils. The last dollar spent on good B increased his utility by 60 utils. Has this person maximized his utility? If not, should he consume more A and less B OR less A and more B?

4. Suppose that Jack and Jill both shop in the same store; therefore, they pay the same prices for X and Y. Will Jack and Jill both have the same marginal rate of substitution? Explain why or why not.

5. Suppose that beer sells for $2 per bottle and burgers sell for $4 each. Jimmy finds that the last burger he ate added exactly as much to his overall satisfaction as the last beer he drank. Has Jimmy maximized his utility? If not, should he have bought more beer and fewer burgers OR less beer and more burgers?

6. Suppose that a person’s indifference curves are graphed with good Y on the vertical axis and good X on the horizontal axis. At this person’s current consumption bundle the slope of their indifference curve is equal to -1/4. The price of good X is $2, and the price of good Y is $6.

A. How many units of good X would this person just be willing to give up to obtain one more unit of Y?

B. How many units of good Y would this person just be willing to give up to obtain one more unit of X?

C. Has this person made an optimal choice? If not should they consume more X and less Y, or should they consume more Y and less X?

Answer 1

1) Utility maximizes at where ,Per dollar marginal utility from last unit from both goods are same.

Per dollar marginal utility of bread=50/2=25

Per dollar marginal utility of butter=80/4=20

So per dollar marginal utility of bread is higher than butter.so consumer is not maximizing utility.

Because bread is giving more per dollar marginal utility,so consumer should increase consumption of bread and Decrease consumption of butter to maximize utility.

2)

Utility maximizes at where ,Per dollar marginal utility from last unit from both goods are same.

Per dollar marginal utility of food=500/25=20

Per dollar marginal utility of clothing=3000/100=30

So per dollar marginal utility of clothing is higher than food.so consumer is not maximizing utility.

Because clothing is giving more per dollar marginal utility,so consumer should increase consumption of clothing and Decrease consumption of food to maximize utility.

3)In other words utility maximizing where last dollar spend on both goods increase utility by same amount.

Because last dollar spend on B increase utility more than last dollar spend on A,so consumer is not maximizing utility.

So consumer should increase consumption of B and reduce consumption of A to maximize utility.

4) Marginal rate of substitution tells how much consumer willing to substitute one good to consume more of another good, to maintain at same utility level. So it depends on preferences of consumer. Only if jack and jill has same preference then their marginal rate of substitution will be same. Otherwise MRS won't be same.