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![Question 8:
Consider a utility function u(1, 2) = √x₁ + √x₂.
1. What is the optimal bundle with P₁, P₂, and income m?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e708fef-8298-4af3-aeac-e8371d2f23ba%2F4fdae826-374c-42e7-a5fc-57c304ec8440%2Fqkx9h8b_processed.png&w=3840&q=75)
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- Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.4. John has a utility for the quantity of sandwiches, Xs, and quantity of burgers, Xp, that he consumes, represented by the following equation: U(X,X) = XX His income is Y = $24. The price of a sandwich changes from X, = $1 to X, = $4 while the price of a burger remains at X, = $6. Solve for the compensating variation and equivalent variation associated with this price increase.
- 2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2\Y/X and MUy = 2\X/Y ) a) Find three different bundles: (X,Y) = (2, 4½), (2, 3), (4, 24) and find the utility they provide John. Plot the three bundles and connect them with an indifference curve. J-L. IIII -+-+- - -4-L 7-T-T-r הרד - דר -LJ-J-L- 1-L -LJ-J-I ---4. Use the following information to calculate Wren's optimal bundle and his resulting utility: IC:U(x,y) = x0.5, 0.5 Px = 1, Py = 4, m = 48A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
- Help meSuppose Paul gets utility from consuming two goods, pizza (P) and soda (S). His utility function is given by U(P,S) = p0.550.5. Paul's income is $20, the price of pizza is $5 and the price of soda is $2. Find Paul's utility maximizing quantities of pizza and soda.Yam has the following utility function for Apples (X1) and Ice Cream (X2), U(X1,X2) = Min{3X1,X2}. Yam likes to get more of both Apples and Ice Cream. Suppose Yam has an income of M = $160 budgeted to be spend on these two goods and the prices of Apples and Ice Cream are p1 =$2, p2 =$1. Yam's optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) Suppose a quantity tax of $1 is imposed on Ice Cream. Yam's after tax optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) Suppose instead of the quantity tax, the government choose to impose a lump-sum tax of $20. After the imposition of the lump-sum tax, Yam's optimal consumption of Apples is and Ice Cream is (Please put your answer in numerical values with no comma or decimal place.) If government would have to impose one of these 2 kinds of taxes, which of these types of tax would be better…
- 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…8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of Y
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