Question

 Use the following table to answer questions 5 and 6 that follow below (Make sure to show all your work for full credit).

Units of Good X	Total Utility of Good X (utils)	Units of Good Y	Total Utility of Good Y (utils)
1	20	1	19
2	35	2	32
3	48	3	40
4	58	4	45
5	66	5	49

(a) If George spends $5 (total) a week on good X and good Y, and if the price of each good is $1 per unit, then how many units of each good does he purchase to maximize utility?

(b) Given the number of units of each good that George purchases in question 4, what is his total utility?

Answer 1

Units of Good X	TU	MU	MU/P	Units of Good Y	TU	MU	MU/P
1	20	20	20	1	19	19	19
2	35	15	15	2	32	13	13
3	48	13	13	3	40	8	8
4	58	10	10	4	45	5	5
5	66	8	8	5	49	4	4

MU = Change in TU / Change in Units

MU/P = MU / Price

To maximize utility two conditions needs to be fulfilled

1) MUx/Px = MUy/Py

2) Budget equation which is 1X + 1Y = 5 where X is number of units of X and Y is number of units of Y.

So the first condition is fulfilling at 3 units of X and 2 units of Y now we will check whether it is fulfilling the second condition which is the budget equation.

1X + 1Y = 5

1(3) + 1(2) = 5

Hence it is fulfilling the budget equation

a) So George will maximize utility by purchasing 3 units of X and 2 units of Y

b) The total utility by purchasing 3 units of X and 2 units of Y will be

Total Utility at 3 units of X is 48

Total Utility at 2 units of Y is 32

Total Utility will be (48 + 32) = 70