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16. Utility functions are simply mathematical representations of preferences.
(a) True
(b) False
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- Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.Is it possible for total utility to increase while marginal utility diminishes? Explain.(A) The unit in which the utility is calculated is ________ (B) Utility measures __________ of the consumer
- 3. 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?24. What is the difference between total utility and marginal utility? Explain.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…
- 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 2.1. Enumerate and explain the properties of Consumer Preference. 2. Illustrate and explain the Utility Maximization1. How would a fresh produce vendor at the farmers' market create the four types of utility (form utility,. place utility, time utility, and possession utility)?
- Consider 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+pPROBLEM (2) A consumer has utility u(x,y) X y This time, I give you the marginal utilities (don't expect it in the midterm!) MUx = over bundles of food (x) and clothing (y). 1 and MUY x² (a) Does the consumer always prefer more food to less? (b) Does she exhibit diminishing marginal utility for food? (c) Does she exhibit diminishing MRS? (d) If she is indifferent between the bundles A = ( = = The more food she has, does she value food less relative to clothing? (That is, she is willing to give up fewer units of clothing for an additional unit of food) Circle: YES / NO Are her indifference curves bowed towards the origin? Circle: YES / NO ¹) and B = (¹,x), calculate x. , 3 4 1 y² (e) Does she value food -relative to clothing- the same at bundle A and B ? If not, at which bundle does she value food (relative to clothing) more? (f) Why should we not be worried about the fact that the utility function here always takes "negative values"? (g) (wait for the next class for us to cover utility…Consider a consumer whose preferences can be represented by the utility function u(x, y) = x + y (a) Originally, px = 1, py = 2 and m = 1. What bundle does the consumer choose, and what is his utility from this bundle? (b) The price of good x then rises to 3. What bundle does the consumer choose after the price change, and what is his utility from this bundle? (c) Calculate the compensating variation. (Hint: at the new price ratio, what good will he spend his income on?) (d) Calculate the equivalent variation.