Assume that an individual consumes two goods, X and Y. The total utility of each

Question

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 571Total 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.

Explanation / Answer

Marginal utility of 4th item of y is = 135-108 =27
Marginal utility of 5th item of X is = 80-68 = 12
Marginal utility perdollar for 3rd item of X is = 54-38/54 =0.296
Marginal utility per dollar for second item of X is = 78-45/78 =0.423
If the consumer has $420
let px be price of x and py be price of y
x be X items and y be Y items
MRS = y/x = py/px
xpx+ypy =420
MRS = 1.5 ==> y=1.5x
SO we get
130x=420==> x=3 and y = 4.5
SO x=3 and y =4
and if budget is 220
we get 1.69 = x and 2.56 =y
So x= 1 and y = 3

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