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ECO100Y5 Lecture 6: Lecture 6 - October 17, 2017

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pearrabbit974
10 Dec 2017
School
UTM
Department
Economics
Course
ECO100Y5
Professor
Zachary Mahone

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ECO100Y5 Full Course Notes
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Document Summary

I(cid:374)differe(cid:374)(cid:272)e curves, i(cid:374)(cid:272)o(cid:373)e/su(cid:271)stitutio(cid:374) effe(cid:272)ts o(cid:374) de(cid:373)a(cid:374)d, giffe(cid:374) goods. Indifference curves represent all bundles of two goods that provide the exact same utility. Each point on the curve is a bundle with varying amounts of the two goods. Consumer is indifferent between any 2 points on this indifference curve. If there was an indifference curve above this one, then they would prefer all points on that curve. Slope of indifference curves are known as the. If the indifference curve is generated by utility function u(x, y) then the mrs is: (cid:1801)(cid:1818)(cid:1807)(cid:1814)(cid:1801) (cid:1792)(cid:1801)(cid:1820)(cid:1805) (cid:1815)(cid:1806) (cid:1793)(cid:1821)(cid:1802)(cid:1819)(cid:1820)(cid:1820)(cid:1815)(cid:1814)= ood. Ood (cid:1801)(cid:1818)(cid:1807)(cid:1814)(cid:1801) (cid:1792)(cid:1801)(cid:1820)(cid:1805) (cid:1815)(cid:1806) (cid:1793)(cid:1821)(cid:1802)(cid:1819)(cid:1820)(cid:1820)(cid:1815)(cid:1814)= marginal utility of ood. A budget line represents all (apple, orange) bundles that exhausts the budget (w). 2 optimality conditions: mu(cid:3051)p(cid:3051) =mu(cid:3052)p(cid:3052, the whole budget is used. 2 graphical optimality conditions: be on the highest indifference curve, be tangential to the budget line. Tangential when mrs (slope of indifference curve) is equal to p(cid:3051)p(cid:3052) (slope of budget line)!

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Related Questions

Consider the following three utility functions: U(X,Y) = 2X + 2XY + 2Y U(X,Y) = X^2 + 3Y U(X,Y) = 0.5ln(X) + 0.5ln(Y) a. Is the assumption that more is better satisfied for both goods? Justify. (6 points) b. Does the marginal utility of good X diminish, remain constant, or increase as the consumer buys more X, holding good Y constant? Justify. (6 points) c. Is the MRS of X for Y diminishing, constant, or increasing as the consumer substitutes good Y for more of good X along an indifference curve? Justify. (6 points)

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) = xayb (Cobb-Douglas utility function)

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

John M. Keynes: U(x,y) = x + yb (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 px and py respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, px = 10 and py = 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, sx, is defined as

(px 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.

Antonio has strictly convex preferences. He is considering buying a bundle A with positive amounts of good X and good Y. Bundle A costs all of his income and the prices are Px=1 and Py=2. At bundle A his MRS=-3/4.

a. If you were to offer advice to Antonio would you tell him to buy more x and sell back some y or buy more y and sell back more x or to do nothing since he is already maximizing his utility. Explain.