An individual consumes products X and Y and spends $30 per time period. The prices of the two goods are $3 per unit for X and $3 per unit for Y. The consumer in this case has a utility function expressed as: U(X.Y) = 0.5XY How much X should this individual consume, given that he is maximizing the utility? ( A)
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- Is it possible for total utility to increase while marginal utility diminishes? Explain.2 3) For each utility function, determine the marginal utility with respect to x, marginal utility with respect to y, and the MRS. (3pts each) a) U(x, y)-3x+2y b) U(x, y) 10x¹/5 y c) U(x, y)=x+ y²Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-3h¹+, where 3 > 0 and p > 0 are parameters. 1+p
- 7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.Hella the Greek's preferences can be described by the utility function U(x, y) = (x^1/2 + 3^1//2)^2. (a) What is the indifference curve for a utility of 49? (b) By how much does utility increase when Hella increases consumption of good y by one (small) unit, when initially U = 49 and x = 1? (c) Holding utility constant at 49, if initially x = 1, how many additional (small) units of y does Hella have to consume if her consumption of x drops by 6 (small) units?On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
- 1- If Isabelle's marginal utility for pizza is 10 and her marginal utility for salads is 2, then Isabelle will choose to eat five times more (a) salads than pizzas . (b) Isabelle will be ready to exchange five salads for a pizza. (c) Both of the above answers are correct. (d) None of the answers above is not correct. 2- Consider a consumer who consumes two goods, good 1 and good2. We denote by p1 the price of the good1 and by p2 the price of the good2. We denote by Um1 the marginal utility of good 1 for the consumer and by Um2 its marginal utility of good 2. The quantity of good 1 that the consumer must give up in order to be able to consume an additional unit of good 2 is equal to: (a) -p1 / p2 (b) -p2 / p1 (c) -um1/ um2 -Um2 / Um1. 3- Consider a consumer who consumes two goods, good 1 and good 2. We denote by q1 his consumption of good 1 and by q2 his consumption of good 2. Graphically, we measure the quantity of good 1 on the abscissa and the quantity of good 2 on the order. Suppose…Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?Quantity X TUx MUX MUX/Px Quantity Y TUy MUY MUy/Py 1 75 1 96 135 60 B 72 185 50 3 234 66 4 230 45 A 4 294 60 270 5 348 54 2.
- Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. Find Alexi's income-consumption curve for slices of bread for incomes between $0 and $21, assuming a price of $1 per slice.Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. In a graph, draw total utility as a function of number of toasted slices, assuming that Alexi buys 1 toaster.. (b) Suppose there are two Bohemian roommates with identical preferences who derive utility from the number of paintings hung on their hotel's walls (X) and the number of granola bars (Y) that they eat. The specific utility function underlying their preferences is given by: U₁ (X,Y)= X1¹³ Y₁23 (for i=1.2) mes Given that each roommate has $300 to spend and P=$100, Py = $ 0.20, explore the consequences of various expenditure allocations. In particular provide a detailed analysis of the possibility leading to free ridership Will that solution be efficient? If so or if not, why? Calculate the efficient allocation. What arrangement for cost sharing would be Pareto superior?