Suppose that a consumer has a choice between two goods, X and Y. If the price of...

Suppose that a consumer has a choice between two goods, X and Y. If the price of X is $2 per unit and the price of Y is $5 per unit, how much of X and Y will the utility maximizing consumer purchase, assuming an income of $19? Use the information on total utility given below. Use a methodology that could be used in answering a more complex problem and show how you used this methodology. Trial and error or summing the different combinations of TU to find the highest are not acceptable approaches.

	TUx	TUy
1	20	100
2	38	175
3	54	120
4	62	140
5	66	145

Solutions

Expert Solution

Income = $19

Price of X = $2

Price of Y = $5

Marginal utility is change in utility of consuming additional unit of a good

Marginal utility per dollar is calculated as (marginal utility of a good / price of that good)

	Total utility of X	Marginal utility of X	Marginal utility per dollar of X	Total utility of Y	Marginal utility of Y	Marginal utility per dollar of Y
1	20	20	10 (3rd)	100	100	20 (1st)
2	38	18	9 (4th or 5th)	175	75	15 (2nd)
3	54	16	8	220	45	9 (4th or 5th)
4	62	8	4	240	20	4
5	66	4	2	245	5	1

Consumer will consume good first whose marginal utility per dollar is maximum and so on.

Consumer will consume 1st unit of good Y due to highest marginal utility per dollar.

Consumer will consume 2nd unit of good Y due to second highest marginal utility per dollar.

Consumer will consume 3rd unit of good X due to third highest marginal utility per dollar.

Consumer will consume 4th or 5th unit of good X or Y due to equal utility of X and Y marginal utility per dollar.

Thus, consumer will consume 3 units of good Y and 2 units of good X which result in total expenditure of $5 * 3 + $2 * 2 = $19.

Rahul Sunny answered 1 year ago

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