Homework Answers
Answer 2. a.
b. Budget constraint: 20=2x+2y
c. (x*,y*)= (4,6)
as IC intersect BL at this point.
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2. Sandra has the following preferences over cookies (x) and tea (y) (x,y) = min(3x, 2y)...
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2. Zhixiu has the following linear preferences over coffee (x) and candy (y): u(x, y) = 2x+4y (a) Graph the indifference curves for Zhixiu that represent each of the following utility levels: 10, 20, 40, and 60. (You should be drawing 4 indifference curves, make sure to label with one represents which utility level) Make sure to show your calculations for how you identified the equation of the indifference curves.(4 points) (b) Setup Zhixiu's utility maximization problem with a general...
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Erin has the following utility over cookies and leisure. U = min(31,c) (Utility) 5 € 4 3 2 1 0 0 0.33 0.67 + 5 1 2 3 4 Her indifference curves are plotted in the above graph. She can choose from the following five bundles for leisure and consumption (l,c): 1. Point 1: (3,3) 2. Point 2: (2,2) 3. Point 3: (1,1) 4. Point 4: (3,2) 5. Point 5: (3,1) a. What is her utility from each bundle? b....
Imagine a representative consumer, whose utility for apples (X) and all other goods (Y) can be...
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1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
7. Mark has linear preferences over plain yogurt and hamburgers described by, U = 4H+ Y,...
7. Mark has linear preferences over plain yogurt and hamburgers described by, U = 4H+ Y, where H is the number of hamburgers, and Yis pounds of yogurt. Fully label your diagram. a. The price of hamburgers, PH - S5/burger, and the price of yogurt, Py = $1/pound. Mark has $80 in income. Putting yogurt on the 'Y' axis, use a graph to show Mark's budget constraint. How do you interpret the slope of the budget line? b. On the...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
4. An individual has preferences over two goods (x and y) that are represented by function...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her i...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her income I = 10. (e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Define corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose). (f)Describeaboutwhatthedualityproblemis. Definemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.) (g) Consider a price increase for the good x from...
2. Zhixiu has the following linear preferences over coffee (x) and candy (y): u(x, y) = 2x+4y (a) Graph the indifference curves for Zhixiu that represent each of the following utility levels: 10, 20, 40, and 60. (You should be drawing 4 indifference curves, make sure to label with one represents which utility level) Make sure to show your calculations for how you identified the equation of the indifference curves.(4 points) (b) Setup Zhixiu's utility maximization problem with a general...
Erin has the following utility over cookies and leisure. U = min(31,c) (Utility) 5 € 4 3 2 1 0 0 0.33 0.67 + 5 1 2 3 4 Her indifference curves are plotted in the above graph. She can choose from the following five bundles for leisure and consumption (l,c): 1. Point 1: (3,3) 2. Point 2: (2,2) 3. Point 3: (1,1) 4. Point 4: (3,2) 5. Point 5: (3,1) a. What is her utility from each bundle? b....
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
7. Mark has linear preferences over plain yogurt and hamburgers described by, U = 4H+ Y, where H is the number of hamburgers, and Yis pounds of yogurt. Fully label your diagram. a. The price of hamburgers, PH - S5/burger, and the price of yogurt, Py = $1/pound. Mark has $80 in income. Putting yogurt on the 'Y' axis, use a graph to show Mark's budget constraint. How do you interpret the slope of the budget line? b. On the...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
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