John has the following utility function: U(X,Y) = 4X²Y. a) Does he believe that more is better for each good? Explain your answer. b) Does his marginal rate of substitution of X for Y (MRS,y) is diminishing, in- creasing or constant as X increases?
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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.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.Philip's utility function is U(q1,q2)=4q10.26+q2. Part 2 Calculate the substitution, income, and total effects for a change in the price of q1 on the demand forq1. The substitution effect for a change in p1 is ε*= .... the income effect is θξ=... and the total effect is ε=... (Round your responses to 2 decimal places and include a minus sign as necessary.)
- 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…Dana's utility function is U(x,y) =3.2 x3.7y7.9. It follows if she has 2.4 units of good X and 1.1 units of good Y, her marginal rate of substitution (of good X in terms of good Y) is equal to ...
- 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.Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つ つ エ B NCompute 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
- Consider a person who consumes two goods, x and y, and has a utility function given by U(x, y) = In(x)+y. This person has an income of $100 and faces a price of $0.50 for good x and $1 for good y. Price of x then rises to $0.60. Solve for the compensating variation (CV) and equivalent variation (EV) of this price change. Show your work.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.