Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, c²) = c(c²)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.
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- 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?10. Utility is a type of function that occurs in economics. When a consumer receives x unils of a certain product, a certain amount of pleasure, or utility U, is derived The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1 , from 1 to 2 , from 2 to 3 , from 3 to 4 b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is (Type an integer or a decimal.)EXERCISE 1Below is a production possibilities table for consumer goods (Food) and capital goods(Robots):A B C D EFood 0 1 2 3 4Robots 10 9 7 4 01. Show these data graphically. Upon what specific assumptions is this productionpossibilities curve based?2. If the economy is at point C, what is the cost of one more food? Of one morerobot? Explain how the production possibilities curve reflects the law ofincreasing opportunity costs.3. If the economy characterized by this production possibilities table and curvewere producing 3 food and 2 robots, what could you conclude about its use ofavailable resources?4. What would production at a point outside the production possibilities curveindicate? What must occur before the economy can attain such a level ofproduction?EXERCISE 2Explain how (if at all) each of the following affects the location of a country’s productionpossibilities curve:1. The quality of education increases.2. The number of unemployed workers increases.3. A new technique…
- 3. Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 5A/4B³/4. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose Pa increase. Show graphically the income, substitution effect and total effect and explain. c. Suppose PA increase. Show the graph for CV and EV and explain.5. A consumer buys only two goods, X and Y. No other goods exist and there is no possibility of saving. The marginal utility of X is independent of the quantity of Y consumed, and the marginal utility of Y is independent of the quantity of X consumed. MUX is constant no matter how he consumes, but MUY falls as consumption increases. In the initial equilibrium he consumes one of each good. How much can you infer about the following:a.) The slope of the indifference curveb.) The curvature of the indifference curvec.) Whether the marginal utility of money is constant, rising, or falling as money income increases.d.) the income elasticity of demand for Ye.) The price elasticity of demand for X.Would you expect total utility to rise or fall with additional consumption of a good? Why?
- If people do not have a complete mental picture of total utility for every level of consumption, how can they find their utility-maximizing consumption choice?Would you expect marginal utility to rise or fall with additional consumption of a good? Why?Jill likes to consume coffee and cream in a very particular way: with every cup ofcoffee she always consumes two 0.5 oz. cream containers. Jill is a utility maximizer anddecides to spend her income is $120 per month on coffee and cream. If the price of eachcoffee cup is $2.50, and the price of each cream container is $0.25, she will consume______ cups of coffee and ______ cream containers per month.A) 48; 96.B) 96; 48.C) 240; 480D) 80; 40E) None of the above.
- 1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…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…Only typed answer and don't use chat gpt and don't answer in table 2. Charlie consumes apples (A) and bananas (B). His utility function is . The price of apples is $1, the price of bananas is $2, and Charlie’s income is $40. The price of bananas suddenly falls to $1. (a) Before the price change, how many apples and bananas did Charlie consume? (b) After the price change, how many apples and bananas did Charlie consume? (c) If after the price change, Charlie’s income had changed so that he could only attain his original level of utility, how many apples and bananas would he have consumed? (d) What are the magnitudes of the price, substitution, and income effects for the consumption of bananas?