# Optimal bundles of goods

For each of the following situations, decide whether the bundle Lakshani is thinking about consuming is optimal or not. If it is not optimal, how could Lakshani improve her overall level of utility? That is, determine which good she should spend more on and which good should she spend less on.

a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater.

b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen would add five times as much to her total utility as the last pencil.

c. Lakshani has $50 per season to spend on tickets to football games and tickets to soccer games. Each football ticket costs $10 and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket.

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#### Solution Preview

a. In this case the bundle is not optimal. Although her marginal utility per pair of sneakers is the same as the same as that for sweaters, but the price difference causes the utility per dollar be to greater for sweaters. In fact the ...

#### Solution Summary

Determine the optimal bundle of goods based on price and consumer's marginal utilities

Find the optimal bundles of consumption.

Assume that an individual consumes two goods, X and Y. The total utility of each good is independent of the rate of consumption of the other good.

The price of X and Y are $40 and $60 respectively. Use the following table of total utilities to answer the following questions.

Good Total Utility of X Total Utility of Y

1 20 45

2 38 78

3 54 108

4 68 135

5 80 159

6 90 180

a. The marginal utility of the fourth unit of Y is _.

b. The marginal utility of the fifth unit of X is _.

c. The marginal utility per dollar spent on the third unit of X is _.

d. The marginal utility per dollar spent on the second unit of Y is _.

e. If the consumer has $420 to spend, _ unit of X and _ units of Y maximize utility subject to the budget constraint. Explain.

f. If the consumer has $220 to spend, _ units of X and _ units of Y maximize utility subject to the budget constraint. Explain.