How can I analyze and find the Marshallian Demands of the following Utility function? u(x)=min{x1,x2}x3 I understand that goods x1 and x2 are perfect complements with each other, but what is the relation with x3?
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![How can I analyze and find the Marshallian Demands of the following Utility function?
u(x)=min{x1,x2}x3
I understand that goods x1 and x2 are perfect complements with each other, but what is the relation
with x3?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c26f867-58cc-4745-bf80-805aafc1d893%2F3c99c364-75ad-42dd-8b9a-0ce06b2f6b1a%2Fguca1od_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.Julie, who has $64, consumes only two goods: whistles (w), which cost $6 each and xylophones (x), which cost $7 each. Her preferences over these two goods can be represented by the utility function u(w, x) = 3w0.75 0.25 a) What is the optimal number of whistles for Julie to consume given this scenario? b) What is the level of utility Julie attains at this level of consumption? c) Suppose now that the price of whistles rises from $6 to $7. What is the magnitude of this price effect on whistles?Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. d. Use the equation from part (c) and the budget constraint from part (a) to find Rick’s demand for each of the two goods. e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick’s budget constraint and indifference curve passing through his chosen consumption bundle. f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.
- Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…Floyd's utility function is given by U(X,Y)=2XY. MUx=2Y and MUy-2X. The price of good X is Px=2, while the price of good Y is Py = 1. Floyd's income is 1,000. Which of the following is true given that the price of good X falls to 1? The substitution effect for good X results in an increase of X consumption by about 1,043 units and a decrease in Y consumption by about 14 units. The substitution effect for good X results in X consumption of about 250 units. The substitution effect for good X results in X consumption of about 500 units. The substitution effect for good X results in an increase of X consumption by about 250 units and no change in Y consumption.*2.2 Guerdon always puts half a sliced banana, q₁, on his bowl of cereal, 9₂ -the two goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and mathematically. (Hint: See Solved
- Cobb-Douglas Preferences] Asad lives in a world with two goods (N=2), apples and bananas. He has a Cobb-Douglas utility function over these goods U(a, b) = a 0.7 b 0.3 . Asad has an income I = 200, and faces prices pa = 2, pb = 1 (a) We know that if Asad is optimizing (and consumes a bundle that contains both apples and bananas), that the slope of the budget constraint should be equal to his MRS. Use this and his budget constraint to solve for his optimal bundle. (b) Suppose the price of apples rises to 4, and the price of bananas rises to 3. What is his new optimal consumption bundle? (c) Suppose Asad instead had a utility function given by U(a, b) = a 1.4 b 0.6 + 1. Given the same prices and income as in part (b), what is his optimal bundle?Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…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…
- You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.The following table shows the amounts of additional satisfaction (marginal utility) that Ross would get from consuming successive quantities of products A and B. a. Fill in the MU/P column for each product. Price of Good A = $8 Price of Good B = $4 Units of Good A MU of Good A, utils MU/P for A Units of Good B MU of Good B, utils MU/P for B 1 56 1 32 2 48 2 28 3 32 3 24 4 24 4 20 5 20 5 12 6 16 6 10 7 12 7 8 If Ross has an income of $28, how many units of each good will he purchase to maximize his utility? ______units of good A ______units of good BBob views apples and oranges as perfect substitutes in his consumption, and MRS = 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is €2 per pound, the price of oranges is €3 per pound, and Bob's budget is $24 per week. What is Bob's utility maximizing choice between these two goods? A. 12 pounds of apples and no oranges B. 8 pounds of oranges and no apples C. 4 pounds of oranges and 6 pounds of apples D. 12 pounds of oranges and no apples Fiona uses her entire budget to purchase food and clothing. The price of food is €1 per unit and the price of clothing is €2 per unit. Fiona's marginal utility from food is 2 and her marginal utility from clothing is 6. She currently spends all her money on food and clothing. Her objective is to maximise her utility. Which of the following statements is correct? Fiona should buy more food and more clothing. A. B. C. D. E. Fiona is currently maximsing her utility and should continue to consume her current…
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