10. Assume that Mr. Ken Cleanaírsystems has marginal utility schedules for good X and Y as given below, that the price of X is $1 and the price of Y is $2. Mr. Cleanairsystems has an income $9. When total utility is being maximized, Mr. Cleanairsystems will buy: a. 7 X and I Y. b. 5 X and 2 Y. c. 3 X and 3 Y. d. 1 X and 4 Y. e. 6 X and 3 Y. Good X mu/$ Good Y mu/$ Quantity_ Marginal Utility Quantity_ Marginal Utility GON Nuo . NOWA 0100

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Nelly StrackeLv2

25 Apr 2018

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Related questions

Given the following details about utility, and prices, please find the quantity at which utility is maximized. (If price of good X is $1 and good Y $2, then marginal utility by price is equal at 1 unit of consumption of X and Y.)

Quantity of X	Total Utility from X	Marginal Utility from X	MU/P (X)	Quantity of Y	Total Utility from Y	Marginal Utility from Y	MU/P (Y)
1	100	100	100	1	250	250	125
2	190	90	90	2	440	190	85
3	270	80	80	3	600	160	80
4	330	60	70	4	700	100	50

Given the following details about utility, and prices, please find the ratio of marginal utility by price for maximizing condition. (If price of good X is $1 and good Y $2, then marginal utility by price is equal at 1 unit of consumption of X and Y.)

Quantity of X	Total Utility from X	Marginal Utility from X	MU/P (X)	Quantity of Y	Total Utility from Y	Marginal Utility from Y	MU/P (Y)
1	100	100	100	1	250	250	125
2	190	90	90	2	440	190	85
3	270	80	80	3	600	160	80
4	330	60	70	4	700	100	50

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = x^ay^b (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + y^b (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, s_x, is defined as

(p_x x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.