Can someone make this for me by today, 22:00 (CET) ?
Microeconomics for Economic Policy Homework Assignment 2 Fall 2022 – Central European University Instructor: Mats Köster Teaching Assistant: Ulrich Wohak Due Date: Friday, October 21, 2022 Individual Demand and Revealed Preferences 1. Juan’s utility function is u(x, y) = xy + 2x. The price of good x is Px, the price of good y is Py, and Juan’s income is I. (a) Find analytically and draw the indifference curves of Juan. (b) Find analytically and draw Juan’s demand function for both goods. (c) Find analytically and draw Juan’s Engel curves for both goods. (d) For each of the two goods, argue whether this good is: i. normal or inferior; ii. ordinary or a Giffen good; iii. a substitute to or a complement of the other. 2. Zoltan likes hot-dogs and hamburgers and is always indifferent between both. Re- gardless of how many hamburgers (or hot-dogs) he has eaten this month, he is indifferent between consuming an additional hamburger and an additional hot-dog. (a) Provide an example of a utility function, which represents Zoltan’s preferences for hamburgers (x) and hot-dogs (y). (b) Represent graphically the indifference curves. (c) What can you say about Zoltan’s preferences for the two goods? 1 (d) Find Zoltan’s demand for hamburgers and hot-dogs as function of the price of a hamburger (Px), the price of a hot-dog (Py), and Zoltan’s income (I). 3. Suppose that Olivia has a weekly income of $30 and only buys apples and oranges. Initially the price of one kilo of apples is $5 and the price of one kilo of oranges is $3. At those prices, Olivia purchases 3 kilos of apples and 5 kilos of oranges per week. Suddenly the price of one kilo of apples goes up to $6 and the price of one kilo of oranges goes down to 2$, whereas her weekly income continues to be $30. At the new prices, Olivia purchases 4 kilos of apples and 3 kilos of oranges. Are Olivia’s observed choices consistent with utility maximization? Substitution and Income Effect 4. Odette consumes apples and bananas only. Her utility function is given by u(xA, xB) = xAxB. The price of apples is $1, the initial price of bananas is $2, and Odette’s daily income is $40. The price of bananas suddenly goes down to $1. (a) Find Odette’s optimal daily consumption bundle before and after the change of the price. (b) Decompose the change of Odette’s daily demand for bananas into the substi- tution effect and the income effect à la Hicks and à la Slutsky. (c) Illustrate graphically the substitution and income effects in both cases. Consumer Surplus and Market Demand 5. The director of a theater company in a small college town is considering changing the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go to the theater into two 2 groups and has come up with two demand functions. The demand curves for the general public (Qgp) and students (Qs) are given below: Qgp = 500− 5P QS = 200− 4P (a) Graph the two demand curves on one graph, with P on the vertical axis and Q on the horizontal axis. (b) Identify the consumer surplus of each group for a price P = 35. (c) Identify the consumer surplus of each group for a price P = 55. (d) Derive and graph the the market demand. Choice under Uncertainty 6. Mats has the choice between two jobs for the next year: either he becomes a professor or a consultant. As a professor, Mats could earn a safe income of $70,000 per year. As a consultant, however, Mats income would depend on the success of the company. In a good year, Mats would earn $120,000, while in a bad year he would earn only $20,000. Good and bad years are equally likely, each occurs with 50% probability. (a) Calculate the expected income and the variance in income as a consultant. (b) Suppose that Mats has currently no wealth and his a utility function over future wealth is given by u(x) = √ x. If Mats chooses the job with the higher expected utility, does he end up as a professor or as a consultant? (c) Now consider Paul, who faces exactly the same two job offers. Also Paul has no current wealth, but his utility function over future wealth is given by u(x) = x2. Which job does Paul choose? (d) Draw the utility functions of Mats and Paul, and discuss their job choices at the hand of this graph. 3