i. Analyze the utility maximizing problem with two goods as follows: Max u(x, y) subject to px + qy = m %3D And obtain Marginal rate of substitution.
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![i. Analyze the utility maximizing problem with two goods as follows:
Max u(x, y) subject to px + qy = m
And obtain Marginal rate of substitution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4904fa6-1644-4cb3-ab51-485987620b40%2F51b6e3ae-835a-4e2b-b9d8-bd884348662c%2F7kj0fyg_processed.jpeg&w=3840&q=75)
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- Suppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25? PLEASE ONLY ANSWER PART C, D AND EAn individual allocates $306 each month to buying two goods, X and Y, in such a way that maximizes their utility U (X,Y) = 2X Y i. Good X costs $4.25 and Good Y costs $17. If MUx = Y and MUy = X2, calculate the substitution and income effect for Good X when the price of Good %3D Y X falls to $3.40. Do not round your intermediate calculations, but you can round your final answers for units of X and Y to two decimal places.Draw a budget line with good X on the x-axis and Good Y on the Y axis. Graphically illustrate the effect of an increase in the price of good X on the utility maximizing quantity of X consumed. Make sure you identify the income effect and the substitution effect. Assume that the good is a normal good. please no shortcut show the whole questions step by step
- 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.1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV
- 1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).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…Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) U(X,Y)= 1- e-ax -e-by b) U(X,Y)= XY + 3X + 5Y c) U(X,Y)= (0.3Xm +0.78m)/1 X1-a y1-b d) U(X,Y)= + 1-a 1-b
- 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 =…Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - suppose a lump sum tax of the same dollar amount, of a 1 pound tax per unit on donuts, is levied on Gino. what is Gino's utility maximising market basket? - why would Gino prefer a per unit tax over the lump sum tax, or vice versa, or why is he indifferent between the two taxes.Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - what is Gino's budget line and what quantities of Qc and Qd will maximise Gino's utitlity? - holding income and Pd constant, what is Gino's demand curve for carrots? - suppose a tax of 1 pound per unit is levied on donuts. how will this alter Gino's utility maximisinzing market basket of goods?
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