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2. Eli's preferences for hamburgers and beer can be described by the utility function U(H, B)min(3H,...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
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...
can be described by the utility function U(r, y)102. Prices Sally the Sleek's preferences are pz...
can be described by the utility function U(r, y)102. Prices Sally the Sleek's preferences are pz 2 and py 4. (a) If Sally initially consumed 10 units of and 5 units of y, how much could she save if she consumed 8 more (small) units of x and kept utility constant?1 Therefore, can it be optimal to (b) Sally decides that she wants a level of U 27. What is the minimum she would have to spend c) What is...
Sally the Sleek’s preferences can be described by the utility function U(x, y) = x^2y^3/1000. Prices...
Sally the Sleek’s preferences can be described by the utility function U(x, y) = x^2y^3/1000. Prices are px = 4 and py = 3; she has an income of $80 to spend. (a) If Sally initially consumed 5 units of x and 20 units of y, how much additional utility does she get from spending one (small fraction of a) dollar more on good x? How much additional utility does she get from spending one (small fraction of a) dollar...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function U(z, y)/1024. Prices are Pz 2 and py 4. (a) If Sally initially consumed 10 units of a and 5 units of y, how much could she save if she consumed 8 more (small units of z and kept utility constant?1 Therefore, can it be optimal to consume the bundle (10,5)? (4) in order to attain that utility? (4) round to two decimal places...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)=...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
John has preferences for food F and clothing C described by a utility function U(F,C) =...
John has preferences for food F and clothing C described by a utility function U(F,C) = min (F, 2C). Suppose that food costs $1 a unit and that clothing costs $2 a unit. John has $12 to spend on food and clothing. (10 pts.) a) On a graph, draw indifference curves corresponding to u = 6, u = 10, u = 14. Make sure to label coordinates clearly. Using the graph, find the optimal choice of food and clothing. Let...
2. Mike's preferences are represented by the utility function U(A, B)- A+2B. He has an income...
2. Mike's preferences are represented by the utility function U(A, B)- A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ii) graph the budget lines for each combination of prices, (iii) calculate and label the optimal consumption choice(s) for each combination of prices, and (iv) calculate the utility Mike derives from consuming the optimal consumption choice bananas (a)...
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x...
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income...
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ü) graph the budget lines for each combination of prices, (i cakculate and label the optimal consumption choice(s) for each combination of prices, and (iv) cakulate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
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...
can be described by the utility function U(r, y)102. Prices Sally the Sleek's preferences are pz 2 and py 4. (a) If Sally initially consumed 10 units of and 5 units of y, how much could she save if she consumed 8 more (small) units of x and kept utility constant?1 Therefore, can it be optimal to (b) Sally decides that she wants a level of U 27. What is the minimum she would have to spend c) What is...
1 Expenditure Minimization (10 points) Sally the Sleek's preferences can be described by the utility function U(z, y)/1024. Prices are Pz 2 and py 4. (a) If Sally initially consumed 10 units of a and 5 units of y, how much could she save if she consumed 8 more (small units of z and kept utility constant?1 Therefore, can it be optimal to consume the bundle (10,5)? (4) in order to attain that utility? (4) round to two decimal places...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
John has preferences for food F and clothing C described by a utility function U(F,C) = min (F, 2C). Suppose that food costs $1 a unit and that clothing costs $2 a unit. John has $12 to spend on food and clothing. (10 pts.) a) On a graph, draw indifference curves corresponding to u = 6, u = 10, u = 14. Make sure to label coordinates clearly. Using the graph, find the optimal choice of food and clothing. Let...
2. Mike's preferences are represented by the utility function U(A, B)- A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ii) graph the budget lines for each combination of prices, (iii) calculate and label the optimal consumption choice(s) for each combination of prices, and (iv) calculate the utility Mike derives from consuming the optimal consumption choice bananas (a)...
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
2. Mike's preferences are represented by the utility function U(A, B) A+2B. He has an income of $20. Consider each of the following combination of prices of goods. On the same graph, (i) graph a family of indifference curves for the consumer, (ü) graph the budget lines for each combination of prices, (i cakculate and label the optimal consumption choice(s) for each combination of prices, and (iv) cakulate the utility Mike derives from consuming the optimal consumption choice. bananas 20...
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