2. Identifying normal, inferior, and Giffen goods Suppose that BC1 on the following graph represents your initial budget constraint for good X and good Y, and point A represents the best bundle, given this choice set. After a change in the price of good X, your new budget constraint is now BC₂. The compensated budget is parallel to BC2, representing the same tradeoff between good X and good Y, and it is tangent to the given indifference curve (U) at point B. GOOD Y * C B BC, GOOD X CB BC₂ ?

2. Identifying normal, inferior, and Giffen goods Suppose that BC1 on the following graph represents your initial budget constraint for good X and good Y, and point A represents the best bundle, given this choice set. After a change in the price of good X, your new budget constraint is now BC₂. The compensated budget is parallel to BC2, representing the same tradeoff between good X and good Y, and it is tangent to the given indifference curve (U) at point B. GOOD Y * C B BC, GOOD X CB BC₂ ?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)0.5 for x₁ > 0, x₂ > 0, and x² > x². 1. Find your marginal utility function for each good.
2. Suppose there are two goods in the economy: Food (F) and Composite good (Y), with Pp = 1 and Py = 2. Consider a consumer who has utility function u(F,Y) = InF + In Y and income I = $100. (a) Find the consumer's consumption choice. (b) Suppose, to promote better nutrition, the government institutes a welfare program that gives every consumer with income less than $500 additional $100. Find the consumer's new consumption choice. How much of the government's payment went into purchasing Food? (c) Suppose rather than giving cash, the government gives a voucher that can only be used to purchase (up to) $100 worth of Food. How does this affect the consumer's consumption choice? (d) Which of the two programs is more effective in achieving the government's goal? Explain.
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Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?
Assume the prices of product X and Y are $1.50 and $1.00, respectively, and that Mr. Chen has $24 to spend. Assume a normal indifference curve. Assume that Mr. Chen needs 4 of product X to maximize utility. a. What is the slope of Mr. Chen's budget constraint. b. Write out Mr.Chen's equation to his budget constraint. c. What combination of X and Y will Mr. Chen purchase? d. Now assume that the price of Y changed from $1.00 to $2.00, redo part a, b and c,
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4. If we have the utility function, U(x)=(x−7)^2, and we know that there is an indifference set around x = 4 and an upper contour set of x = 6. How to graphically represent this function? I'm confused about how to draw the upper contour set on the graph? I know the concept that upper contour is the area over the convex line, but don't know how to put it on the graph. Could you draw a simple graph to help me identify the upper contour?
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6) Indifference curves represent: a) Ability to pay b) Total Utility c) Marginal Utility d) None of the above
2. For the Income-Consumption Line & Engel Curve: (kindly place Good A on the X-axis & Good B on the Y-axis) If the consumer's tastes are given by the Indifference curves schedule and Pa = P1.00, Pb= P1.00 and original budget = P10.00, what happens if budget decreases to P6.00 and then increases to P14.00, assuming that tastes and prices of the two goods are constant. Create the new budget schedules. Plot the 2 new budget lines as well as the original with the 3 indifference curves together and determine the tangency points or LCPC and create the Income- Consumption Line. Create the Engel Curve for each good.
Assume the prices of product X and Y are $1.50 and $1.00, respectively, and that Mr. Chen has $24 to spend. Assume a normal indifference curve. Assume that Mr. Chen needs 4 of product X to maximize utility. a. What is the slope of Mr. Chen's budget constraint. b. Write out Mr.Chen's equation to his budget constraint. c. What combination of X and Y will Mr. Chen purchase? d. Now assume that the price of Y changed from $1.00 to $2.00, redo part a, b and c,