A consumer has the following utility function: u(x) = (xρ1 + xρ2)1/ρ 1. Derive the Walrasian demand function x(p, w) and compute the indirect utility function. 2. Write down the expenditure minimization program.
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A consumer has the following utility function:
u(x) = (xρ1 + xρ2)1/ρ
1. Derive the Walrasian demand function x(p, w) and compute the indirect utility function.
2. Write down the expenditure minimization program.
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- A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.Rui's utility function is Let the price of good X be px, the price of good Z be normalized to $1.00, and U be her level of well-being. What is her expenditure function? Rui's expenditure function (E) is E = 2. U=X+4XZ+Z. PX(U+0.25) 2 - 0.25 (Px +1) · (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the _ character.) Derive her unco pensated demand curve for X. Let Y be her income. Rui's uncompensated demand curve for good X is (Properly format your expression using the tools in the palette.) X=Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…
- 5.5 Suppose the utility function for goods x and y is given by utility = U(x, y) = xy + y. a. Calculate the uncompensated (Marshallian) demand functions for x and y, and describe how the demand curves for x and y are shifted by changes in I or the price of the other good. b. Calculate the expenditure function for x and y. c. Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.A consumer has the following demand function for good 1: x1 = (1/4)(m/p1) The original price of the good is $2 and the consumer’s income is $200. Calculate the substitution effect, the income effect and the total effect for this consumer, when the price of good changes to $1.Description 1. Suppose the utility function for goods x and y is given by utility = U(x, y ) = xy + y. a. Calculate the uncompensated (Marshallian) demand functions for x and y, and describe how the demand curves for x and y are shifted by changes in I or the price of the other good. b. Calculate the expenditure function for x and y. c. Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.
- a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.Suppose that we have a utility function involving two goods that is linear of the form U(x, y) = ax + by. Calculate the expenditure function for this utility function. Hint: The expenditure function will have kinks at various price ratios.The price of a good changes. How could you calculate how much income the consumer would have to lose at the old prices to be as well off as they are at the new prices (equivalent variation)? Calculate the value of the expenditure function at the new prices and original utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the new prices and new utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the original prices and new utility minus the expenditure function at the original prices and original utility Calculate the value of the expenditure function at the original prices and original utility minus the expenditure function at the original prices and new utility Which of the following is NOT a good way to measure a change in consumer welfare from a price change? Find the equivalent variation Find the change in the value of…
- Suppose that an individual consumes two goods X and Y, and his direct utility function is given by: U(X, Y) = X" + Y"s. a) Derive the Marshallian demand functions for X. b) Derive the Marshallian income elasticity of good X.The question is an expenditure minimization question. The answer should be very detailed and clear, THANK YOU!!!Khamzat consumes burgers (x1) and sodas (x2). Consider the CES utility function u(x1, x2) = (x + x)UP), for a constant p > 0, where the price of burgers is 20 and soda is 2. Khamzat's income is 100. What is the demand functions for burgers and sodas? Khamzat becomes famous and the store owner recognizes him and decides to give him the burgers at cost, $12. What is the income and substitution effect?
