Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function...
Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function is u(x1; x2) = x1x2. Her income is m = $200. The prices for the two goods are p1 = $20 and p2 = $10 respectively.
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Find Annaís optimal consumption bundle. Show the complete calculations, and illustrate your answer graphically (draw the indi§erence curve and the budget constraint).
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How would your answer change to part (a) if Annaís utility function were given by v(x1; x2) = 4x21x2? Explain.
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Compute Annaís marginal rate of substitution (MRS) at the optimal consumption bundle and give an interpretation.
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Now suppose the government levies a 25% tax on each bottle of wine purchased. Find Annaís optimal consumption bundle and illustrate it in the same graph that you drew in part (a).
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Would Anna prefer a $20 income tax (i.e., lump-sum tax) to the 25% value tax on wine? Which scenario would the government prefer? Justify your answers.
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Anna spends all her income on wine (good 1) and cheese (good 2).
Her utility function...
Mort’s utility function is U(x1,x2) = x1x2. His income is $200. The price of good 2...
Mort’s utility function is U(x1,x2) = x1x2. His income is $200. The price of good 2 is $10. Good 1 is priced as follows: The first 12 units cost $10 per unit and any additional units cost $5 per unit. What consumption bundle does Mort choose? 1) x1 =18, x2 = 6 2) x1 =10, x2 = 10 3) x1 =14, x2 = 7 4) x1 =12, x2 = 8
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Margaret spends all of her income on t-shirts (x1) and shoes (x2). Her preferences can be represented by the utility function u (x1, x2) = 2√x1x2 (a) [15 Points] Derive the demand functions for t-shirts and shoes in terms of the price of t-shirts (p1), the price of shoes (p2), and income (m). Show your result on a graph. (b) [10 Points] Draw the Income Offer Curve and Engel Curves (one for each good). (c) [10 Points] Draw the Price...
John earns $120 per week and likes to consume wine and cheese. His utility function is...
John earns $120 per week and likes to consume wine and cheese. His utility function is of the form ?(?, ?) = (? ^1/2)(? ^3/2) where x denotes the amount of cheese consumed and y the amount of wine. His marginal utilities are ??? = (? ^3/2) / (2? ^1/2) and ??? = (3? ^1/2)(? ^1/2) / 2 d. The price of a bottle of wine is $10 and the price of a piece of cheese is $3. What is...
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Question 2: Lorelai's choice behavior can be represented by the utility function u(x1, 2)0.9Inx)0.1x2 The prices of both x1 and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set but at least linear in good x2) the preferences and parameters accordingly as given in the question. Click...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it...
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently $360. Consider that the price...
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5. A consumer has income of $3,000. Wine costs $3 per glass, and cheese costs $6 per pound. a. (0.5 pt) Draw the consumer’s budget constraint with wine on the vertical axis. (Make sure to label the axes.) b. (0.1 pt) What is the slope of the budget constraint? c. (0.1 pt) On the graph for part a, draw an indifference curve illustrating an optimum bundle (point K). d. (0.4...
An individual has a utility function given by U = x1x2 Marginal Rate of Substitution is...
An individual has a utility function given by U = x1x2 Marginal Rate of Substitution is –x2/(x1) and therefore the Demand function for good 1 is x1= m/(2P1) Assume m=$42, P1=$1, P2=$1 (m=income, P1 is the price of good 1 , P2 is the price of good 2) Calculate the quantity of good one in the optimal choice bundle (x1A)
Question 2: Lorelai's choice behavior can be represented by the utility function u(x1, 2)0.9Inx)0.1x2 The prices of both x1 and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set but at least linear in good x2) the preferences and parameters accordingly as given in the question. Click...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
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Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
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