Now suppose that the relevant budget constraint is I2. Would the individual choose B? Why? 3. Suppose that bundle A in the following figure is chosen by a rational individual (who respects the revealed preferences axiom) when the relevant budget constraint is Ij. (a) Is A revealed preferred to B? (b) Suppose that the relevant budget constraint is I3. Would the individual choose B? Why?

Now suppose that the relevant budget constraint is I2. Would the individual choose B? Why? 3. Suppose that bundle A in the following figure is chosen by a rational individual (who respects the revealed preferences axiom) when the relevant budget constraint is Ij. (a) Is A revealed preferred to B? (b) Suppose that the relevant budget constraint is I3. Would the individual choose B? Why?

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.
B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…
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.
sketch a person’s indifference map and budget line for two goods, X on the horizontal axis and Y on the vertical axis. Mark the optimum consumption point. Now illustrate the following (you might need to draw a separate diagram for each): (a) A rise in the price of good X (a normal good), but no change in the price of good Y. (b) A shift in the person’s tastes from good Y to good X. (c) A fall in the person’s income and a fall in the price of good Y, with the result that the consumption of Y remains constant (but that of X falls).
2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.
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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Suppose Jeff has a perfect substitute preferences for watching movies (M) and TV (T) shows. Jeff's MRSTM is such that he is always indifferent between watching one movie and five TV shows independent of the amount of goods consumed. Which of the following statements is true? If Jeff had a choice between 1 movie and 1 TV show before bed, he would choose to watch the movie. If Jeff has already watched 3 movies and no TV shows, then he would prefer to watch a TV show next. He is indifferent between watching 1 TV show or 1 movie before bed. Jeff would prefer watching 2 TV shows and no movies over watching 2 Movies and no TV shows.
part C D
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