(b) A consumer has $280 to spend on two commodities, the first of which costs $2 per unit and the second $5 per unit. Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second is given by U(x,y) = 100x0.25y0.75 How many units of each commodity should the consumer buy to maximize utility? Compute the Lagrange multiplier a and interpret in economic terms.
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- Joe is currently in consumer equilibrium by consuming cheese and crackers, such that the last cracker consumed yielded 8 utils and the last piece of cheese consumed yielded 12 utils. Assume the price of crackers is two cents per cracker and the price of cheese is three cents per piece. If the price of crackers increases to four cents, Joe should his consumption of crackers and his marginal utility from crackers will and also his consumption of cheese and his marginal utility from cheese will (Assume he is in the downward sloping portion of the MU curve.) Ο Ο Ο decrease; increase; increase; decrease increase; increase; increase; increase increase; decrease; increase; decrease increase; increase; decrease; decreaseGiven the following utility functions for Consumer A and Consumer B and their budget contraints: UA = X0.5Y0.5 UB = X0.2Y0.8 I= Px (X) + Py(Y) and given that: Px = 3, Py= 6 and I = 100 Fill in the blanks in the following table (round to two decimal places): Part 1: Part 2: Part 3: Part 4: For Consumer A, what is the optimal choice of X? Number For Consumer A, what is the optimal choice of Y? Number For Consumer B, what is the optimal choice of X? Number For Consumer B, what is the optimal choice of Y? NumberLisa consumes only two goods, pizzas and burritos. In equilibrium, her marginal utility per slice of pizza is 10 and her marginal utility per burrito is 8. Instructions: Enter your answer rounded to two decimal places. If a slice of pizza costs $3, then the price of a burrito must be $
- Paolo enjoys consuming both soda and coffee. Each can of soda costs Ps = $1, and each cup of coffee costs Pc = $2. Suppose that Paolo buys 75 cans of soda and 50 cups of coffee per month. The following graphs show his marginal utility curves for soda and coffee. At his current consumption level, Paolo's marginal utility from consuming the last can of soda he bought is MUS = 12 utils per can, and his marginal utility from consuming the last cup of coffee he bought is MUC = 12 utils per cup. 24 20 20 16 25 50 75 100 125 150 25 50 75 100 125 150 SODA (Cans) COFFEE (Cups) Is Paolo currently maximizing his utility? O No; he likes coffee and soda more than other goods, so he should buy more of both. O No; he could buy less soda and more coffee, not spend any more money, and be better off. O Yes; the marginal utility he receives from his last can of soda equals that of his last cup of coffee. O No; he could buy more soda and less coffee, not spend any more money, and be better off. MU OF SODA…Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.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…
- Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.Jose has utility for UC Davis sporting events equal to U = S²B where S is the number of Soccer games and B is the number of baseball games. Baseball games cost $5 per game and Soccer games cost $10 per game. How many soccer games will Jose attend in his optimal bundle for ever baseball game? In other words, in his optimal bundle, S = xB. Second, if Jose has $90 to spend on sports, how many baseball games will he attend? In other words, Jose will attend baseball games in his optimal bundle. Third, if Jose's budget increases to $180, now how many baseball games will he attend? Jose will attend baseball games. Fourth, for Jose, is baseball a normal or inferior good? Enter the word "normal" or "inferior" hereAssume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
- The table shows the total utility (TU) that James receives from consuming different amounts of two goods X and Y, per month. Quantity TUx MUx MUx/Px TUy MUy MUy/Py 0 0 0 0 0 0 0 1 50 50 16.67 75 75 25.00 2 88 38 12.67 117 42 14.00 3 121 33 11.00 153 36 12.00 4 150 29 9.67 181 28 9.33 5 175 25 8.33 206 25 8.33 6 196 21 7.00 225 19 6.33 7 214 18 6.00 243 18 6.00 8 229 15 5.00 260 17 5.67 9 241 12 4.00 276 16 5.33 d.How much total utility will James experience by buying the utility-maximizing combination? e.Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?Enrique is a movie buff. He likes to watch on demand movies from his cable company, which cost $5 each, and so likes to go to the local movie house, which charges $15 a ticket. Suppose that given his budget and his tentative spending plans, the marginal utility from a cable movie is 15 utils and the marginal utility of a movie at the local cinema is 45 utils. Assuming he is spending his entire budget, Enrique is currently maximizing his utility Enrique can increase his utility by buying more cable movies and watching fewer cinema movies Enrique can increase his utility by buying more cinema movies and fewer cable moviesElizabeth makes $200 a week at het summer job and spends her entire weekly income on new running shoes and jeans, since these are only two items that provide utility to her. Furthermore,Elizabeth insists that for every pair of jeans she buys, she must also buy a pair of shoes. (without the shoes, the new jeans are worthless). Therefore, she buys the same number of pairs of shoes and jeans in any given week. a) If jeans cost $20 and shoes cost $20 , how many will Elizabeth buy of each?b) Suppose that the price of jeans rises to $30a pair , how many shoes and jeans will she buy?c) To what effect (income or substitution) do you attribute the change in utility levels between part a and part b