Question

Assume that Andy consumes two goods X and Y. His total utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X and Y are, respectively, $5 and $10. Units of the Good Total Utility of X Total Utility of Y 1 2 3 4 5 6 7 8 50 95 135 170 200 225 245 260 400 750 950 1100 1220 1320 1400 1450 a. If Andy is given $65 to spend, how many X and Y will he consume daily? Show your work. b. If his budget increases to $110, what combination will the person consume? Show your work.

Answer 1

Q	TUx	MU/P	TUy	MU/P
1	50	10	400	40
2	95	9	750	35
3	135	8	950	20
4	170	7	1100	15
5	200	6	1220	12
6	225	5	1320	10
7	245	4	1400	8
8	260	3	1450	5

MU (nth unit) = TU (n units) - TU ((n-1) units)

a)

Andy would maximize his utility by spending on units such that those units are selected first where MU/P is maximum.

Budget constraint: 5X + 10Y = 65

X = 1 and Y = 6

MU/P (X) = MU/P (Y) = 10 (utility maximization condition)

a)

Andy would maximize his utility by spending on units such that those units are selected first where MU/P is maximum.

Budget constraint: 5X + 10Y = 110

X = 6 and Y = 8

MU/P (X) = MU/P (Y) = 5 (utility maximization condition)