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Calculating 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.

Solution Preview

Please refer attached file for better clarity of tables.

Good Total Utility of X Total Utility of Y Marginal Utility* MU per dollar spent
TUx TUy MUx MUy MUx/Px Muy/Py
1 20 45 20 45 0.50 0.75
2 38 78 18 33 0.45 0.55
3 54 108 16 30 0.40 0.50
4 68 135 14 27 ...

Solution Summary

Solution depicts the steps to calculate the optimal bundles of consumption subject to given levels of budget.

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