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- 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…Consider the market for a single network good and suppose thatconsumers differ in their valuation of both the stand-alone and thenetwork benefits (it can indeed be argued that it is more plausiblethat a user who has a higher value for the stand-alone component of atechnology also assigns more importance to the size of its network.) Tocapture this idea, write the consumer’s utility function for joining thenetwork as U(θ) = θ(a + νne), where a is the stand-alone benefit, ν > 0measures the network effect, neis the expected number of users joiningthe network, and is uniformly distributed on the unit interval.a. What happens if p > a + νne? (Hint: Identify all consumer who buythe good for at price p and a given expected network size ne).b. What is the consumer’s willingness to pay for the nth unit of thegood when ne units are expected to be sold? Is the demand downwardsloping? Does the demand increase with the expected network size?c. Express the fulfilled-expectations demand curve…7 Asen tries to minimize his cost of using two goods x subscript 1 end subscript and x subscript 2 end subscript. The price of the first good is BGN 12 and the second good BGN 8. His utility function is x subscript 1 superscript 3 divided by 5 end superscript x subscript 2 superscript 2 divided by 5 end superscript and the utility he will get from using both goods, is 32 units. Find the Hicks quantities demanded and what Assen's minimum budget must be to consume these quantities and obtain the above utility. e-412, h2=21, h1=21 e=416, h2=21, h1=21 e=640, h1=32, h2=32 e=422, h2=21, h1=21 e=378, h2=21, h1=21 e-378, h2=20, h1=20 another answer e-378, h2=24, h1=24
- . Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.QUESTION 6 Which of the following was insight regarding optimal pricing that we gleaned from behavioral economics? O Make costs lump sum (integrate the costs into one cost) and separate allof the benefits of a purchase (separate the gains from an exchange). O Consumers always act rationally in their consumption decisions. O Expectations about products' prices don't matter for consumer behavior - all that matter's is the price they actually face, O Default choices for consumers don't matter for their behavior. QUESTION 7 Which of the following are the conditions for a firm to be able to profitably engage in bundlhpg?. O There is variation in consumers' willingness and abilities to pay for the goods, and consumers' valuations of the goods are positively correlated. O Consumers must like the bundled goods relatively equally. Consumers' preferences across the goods are relatively consistent with each other. O There is variation in consumers' willingness and abilities to pay for the goods,…Which among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistent
- fonsumer's demand xy for two different and the consumer's in come is $72. different Consumer's demand xy for chosen to maximize two the శ్రిందికి goods are x² lefility function The per respectively unit of , and the Consumer's in come is $7 x and y are $3and $4. 22,2 © telrite out the fagrangean for the Constrained maximization problem © Find the utility maximizing demands for both goods and he Larange multiplier, 2 o What is the change in consumer's ufility if income Changes from $72 to $75Generally speaking the demand for a good will be more inelastic O if the good is very specific and narrowly defined. O the greater the time period being considered. O if the good is a luxury. O if the good makes up a small part of an individual's budget. 21 ttv MacBook Pro F8 F9 F7 D00 F4 F6 F5 F32) Explain how utility could be used in a decision where performance is not measuredby monetary value.
- please only do: if you can teach explain each partc: what does it mean? can you show graphs: show WARP : If the consumer’s wealth is high enough that both bundles can buy with both prices then WARP violates If the consumer may not be spending all of her wealth, are her choices consistent withthe Weak Axiom of Revealed Preference (or is it impossible to determine)?: If the consumer’s wealth is high enough that both bundles are aordable atboth prices then WARP violates. why? Therefore, it is notpossible to know2. A consumer has a utility fuinction given by a) Derive an expression for the two marginal utilities: MU (x1, 22) and MU2 (21, r2). Since AMRS = -YU use these marginal utilities to derive a simple expression for the MRS (r1, 22). b) Optimal choice on the part of the consumer implies MI RS = -. Suppose M 20, p1 = p2 = 1. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. c) Now keep income at 20, and pi = 1, but set p2 - 2. Show the optimal choice in this case on a well-labelled graplh of the budget set. Inclnde an indifference curve consistent with these preferences.a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?