= Suppose Ashley has the utility over two goods X and Y as U(X,Y)= XY and the prices and income are p = 3, Py 5 and I = 50. Let s, and sy be the shares of income spent on good X and good Y, respectively, and let er, and ey, be the income elasticities of demand for goods X and Y, respectively. Then, Sex,1+Syey, is equal to (a) 2 (b) 1 CORRECT ANSWER (c) 0 (d) -1 (e) Not enough information

= Suppose Ashley has the utility over two goods X and Y as U(X,Y)= XY and the prices and income are p = 3, Py 5 and I = 50. Let s, and sy be the shares of income spent on good X and good Y, respectively, and let er, and ey, be the income elasticities of demand for goods X and Y, respectively. Then, Sex,1+Syey, is equal to (a) 2 (b) 1 CORRECT ANSWER (c) 0 (d) -1 (e) Not enough information

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.3P

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Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?
Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2.
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Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function:U (H, C) = √HCThe average price for the hokey course is 20 dollars and for chess course16 dollars. Moreover, Jack has a budgetof 80 dollars. c) Find the income level which is necessary to make Jack reach the same utility level as before theprice change.d) Compute the quantities demanded with the new prices and the income you found in section c.e) Compute the quantities demanded with the new prices and the original budget of 800 dollars.
The demand for good X is given by Qd = 6,000 – 1/2 Px – Py + 9Pz + 1/10 M Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100 while the average income of individuals consuming this product is M = $70,000. A. Indicate whether goods Y and Z are substitutes or complements for good X. B. Is X an inferior or a normal good? C. How many units of goods X will be purchased when Px = $5,230? D. Determine the demand function and the inverse demand function for good X. Graph the demand curve for good X.
Please no written by hand solutions Bunter’s preferences over a bundle consisting of x1 units of good 1 and x2 units of good 2 are represented by the utility function U (x1, x2) = 2√x1 + √x2. Bunter faces prices p1 = 4, p2 = p, and he has an income of I = 16. 1. Is Bunter’s utility function quasi-concave? 2. Find Bunter’s demand function for good 1 and good 2 as a function of the price p. 3. What is Bunter’s marginal utility for income? 4. Suppose the price of good 2 increases from p2 = 2 to p2 = 3. What is the income and substitution effect of this price change? If the government wanted to maintain Bunter’s original utility by giving him a cash subsidy, how much should it be? 5. Suppose that, as in part (4), the government wanted to maintain Bunter’s utility after the price increase. However, the government does not know Bunter’s preferences. As a consequence, to compensate for the price increase, the government decides to give a cash subsidy just sufficient so that Bunter…
Pankti consumes two goods, x and y. Her utility function is given byU(x, y) = ln(xy).(a) Are Pankti’s preferences homothetic? Explain.(b) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6units of good y. Without solving for Pankti’s Marshallian demands for x and y,determine how her consumption of x and y would change if her income doubled(holding constant the prices of the goods). Justify your answer as well as you are able.(c) Find an expression for Pankti’s indirect utility function, V (px, py, m), using themethod of Lagrange multipliers. Confirm your answer to part (b) using theMarshallian demands you derive in the process of solving the optimization process.(d) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utilitywhen her income is 24. Now suppose the price of good x doubles to 4. How much extraincome does Pankti need to obtain the same level of utility she had prior to the priceincrease?
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A consumer has preferences over two goods, denominated by x and y, given by the utility function U(x,y) = min{αx,y} with α > 0. The prices of the good are px = 2 and py = 5. The consumer has an income of I > 0. (a) Provide an intuition for this utility function. Specifically, are these goods substitutes or complements? If x is bicycle tires and y is bicycle frames, what is the value for α? (b) For what values of α will the consumer demand (i.e., Walrasian demand) more x than y. (c) For what values of α will the consumer spend more on x than on y (given her Walrasian demands).
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Draw the following scenario: Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ? 1to ? 2, and that she perceives jewelry as a Giffen good in the price range from ? 2to ? 4. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph. The graph may be something like this: