Assume that Sarah's preferences can be represented by the following utility function: U (x, y) = x√y and that her budget is given by pxx+pyy = 1. What is the Marginal Rate of Substitution of x for y? Provide the Demand Function for x and
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Assume that Sarah's preferences can be represented by the following utility function: U (x, y) = x√y and that her budget is given by pxx+pyy = 1. What is the Marginal Rate of Substitution of x for y? Provide the Demand Function for x and the Demand function for y
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- Joyce drinks both coffee (x) and tea (y). Her preferences over these two goods can be represented by the utility function U(x,y) =x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of cups of tea. a) Given her preferences, find her demand functions for coffee (x) and tea (y). b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and tea. Write her demand curve for tea. Illustrate her demand curve. c) Suppose that the price of a cup of tea is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question, assume that her income rises to $60 and that the prices of coffee and tea are unchanged at = $4 and =1.A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?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?
- 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…Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.Dev likes to consume scones (Good X) and cups of coffee (Good Y). Her utility functionis: U(x,y) = min{x, 2y}That is, her level of utility for any given bundle (x,y) is the lesser of x and 2y.Suppose the price of scones is $3 and the price of coffee is $2. Dev’s weekly budget is$20. Determine her optimal consumption bundle for a week.
- Laura's preferences over commodities X₁ and x₂ can be represented by U(x₁,x2)=min{3x₁, x₂}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1. There are both income and substitution effects of this price change. There is an income effect but not a substitution effect of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1 as a result of the increase in p1.Suppose Mia's utility function on lemon soda (X) and chips (Y) is given by U(X,Y) = X0.5Y0.5 She has $80 per month to spend on lemon soda (X) and chips (Y). The prices of lemon soda (PX) and chips (PY) are $2 and $4 respectively.a. Solve for her optimal consumption bundle of lemon soda (X*) and chips (Y*)? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) : b. Suppose the price of lemon soda (X) increases to $8, what is the new optimal bundle? i. Optimal Consumption in lemon soda (X*) : ii. Optimal Consumption in chips (Y*) :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…
- 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.5. Julio who consumes two goods Food (F) and clothing (C) has a utility function given by U(F,C)= sqrt(F)C. The price of food is $3 and the price of clothing is $5 and Julio's weekly budget for food and clothing is $100. a. What is Julio's MRSFe (marginal rate of substiution of food for clothing) when utility is maximized? Explain. b. If Julio is at point where MRSFC= 1, where is that point relative to the utility maximzing bundle (show this in a diagram)? c. Can Julio change his bundle so as to increase his satisfaction and if so in what way? Explain fully Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.