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![Example: U(X,Y) = (XY)-5, Px =2, Px = 1, M = 10
• What will be the consumer's optimal consumption?
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- 1. A consumer wishes to maximize the utility U(X1, X2) = (X1 + 20)(X2 + 30) subject to the available income (M= 600) and prices (pi = 5, p2 = 4). Find the optimal consumption levels and marginal utility of income. ASsuming a local maximum is attained, prove that it is also a unique global maximum.1. Jan has the following utility function for broccoli: U(B) = 54B - 0.5B³ a) What is Jan's marginal utility function?Question 1: Find the expenditure function for a consumer with each of the following utility functions. a. U(X1,X2) = min{X1,X2} b. u=(x,y)=0.5x,0.5y c. U(X1,X2) = X1 + X2
- 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.?Q11. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case A, Total income is $120 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space.The relationship between a consumer's monthly income and monthly consumption of four products, A-D, is shown in the following table. Income $ 5,000 6,000 A 70 64 Quantity Consumed B 35 42 C 10 16 D 20 12 Which product(s) listed is(are) an example of an normal good?
- Please draw the income-consumption (or income-offer) curve for each of the following utility functions, indicating the slope of each: (a) U = (A)(x^a)(y^b) (b) U = min(ax, by) (c) U = ax + byYou 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.Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
- (a) A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less, with diminishing MRS) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her new optimal X consumption? (b) Forget about (a). A consumer with I=$240 budget is shopping for apples (x) and oranges (y). Apples cost $1 each up until 60 units; thereafter each apple costs $2. Similarly, oranges cost $1 each up until 60 units, and thereafter $2 each. Draw the graph of feasible set of bundles for the consumer with relevant points and numbers (shade the feasible area), no explanation needed. (c)(HARD!) In (b), calculate the optimal bundle assuming the consumer’s utility function is u(x,y) = x5y.Suppose your total benefit from eating slices of pizza (value in dollars) is 8x−x^2, where x is the number of slices of pizza. Pizza is sold by the slice and costs $2 per slice, and so the total cost of pizza is 2x. Using optimization in levels, what is the optimal amount of pizza for you to eat?
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