A1: PERFECT SUBSTITUTES..(a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 andY = 10? Create a table then graph/sketch the indifference curve through (10, 10).(b) What do we mean by a composite good? What does this composite good look like with thesepreferences? Show and explain.(c) State the consumer's utility maximization problem and express this in words. Sketch this in afigure and explain.(d) Show that demands are: X = 3M/[3Px + Py] and Y = M/[3Px + Py]. Hint: use the compositegood from (b).(e) Let prices be Px = $5, Py = $3 and income M = $1000. What is optimal X, Y, and utility? Showyour work.(f) Suppose Px rises to $6 and Py falls to $2 but income stays at $1000. Calculate the CompensatingVariation that ensures the consumer is no worse off nor better off with these price changes.Show and explain your work.A2: RISK and INSURANCE...Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house.EVENTFIRENO FIREPROBABILITY OUTCOME INSURANCE PAYOUT$100$5000.020.98$4000PREMIUM????(a) What do we mean when we say an agent is Risk Averse?(b) Assume utility is U(x) = V(x). Why does this utility function imply the agent is risk-averse? Use afigure/diagram to explain.(c) What is the expected payoff and expected utility of having no insurance for this agent?(d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance?(e) What is the maximum the agent will pay for complete insurance that pays out $400 in the caseof fire? Show your work.(f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximumthe agent will pay for insurance now? Show your work and explain relative to (e). Note: I aminterested in your solution technique more than the answer. So show your thought process.

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A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.

A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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5. Suppose a preference relation is represented by a utility function u(x₁, x₂) = x₁ + x₂. Explain why the function -u(x₁, x₂) = −x₁ - x₂ does not represent the same preference relation. It is enough to explain using two appropriate bundles.
) Suppose there are two goods, X and Y. The price of good X is $5, the price of good Y is $3, and your income is $60. Neatly graph your budget line and label the intercepts. (a) What is the slope of your budget line? (b) How many units of good Y do you give up per unit of good X? (c) Suppose the price of good X rises to $6, show what happens to the budget line and label any new intercepts. (d) What is the new slope of the budget line? How many units of good Y do you now give up per unit of good X? (e) Suppose the price of good X only rises to $6 once you have purchased six units of good X. In other words, it is $5 per unit for the first six units and $6 per unit thereafter. Make a new graph of this "kinked" budget constraint.
5) Consider indifference curves for the consumption of milk and chocolates (you may assume that both are 'goods'). The indifference curves are drawn with the number of chocolate bars on the horizontal axis and pints of milk on the vertical axis. Suppose that at every point, consumer A's indifference curve is flatter than consumer B's. What can you conclude about consumers A and B tastes and preferences?
4. Suppose the consumer's utility u: X → R is strictly conver-i.e. such that any x, y EX with ry and any 0 u(λx + (1 − A)y). (a) Show that the consumer will do one of the following: . Buy nothing. . Spend all their money on good 1. • Spend all their money on good 2. [Hint: The previous question could be helpful.] (b) Suppose that, in addition to behig strictly convex, u is increasing. Explain why the consumer will spend all their money on one good.
10) Figure 1 shows some indifference curves and budget lines for consumer Yusuf. Milk A B Cheese Figure 1 If Yusuf's income increases, his optimal consumption changes from point A to point B. Which of the following statements is true for Yusuf? (a) Cheese and milk are substitutes. (b) Cheese is an inferior good. (c) Milk is an inferior good . (d) Milk is a normal good. (e) None of the above.
6 If someone has an income of 20 and he wants to buy Pepsi and hamburgers. Hamburgers are sold in an unusual way. There is only one supplier and the more hamburgers he buys, the higher the price per unit. So, hamburgers cost is a total of 2h^2 (squared) for hamburgers. Pepsi is sold at a price of $2. 1. In this case, write out the budget constraint of hamburgers and Pepsi. 2. His utility function is u(h,p) = 12h + 4p. Draw his 1) budget line and 2) a few indifference curves on a graph. 3. What is the optimal bundle for him?
Letter B. Only.
15. Higher Indifference curve means: (a) Consumer has more income (b) Price of goods have reduced (d) All of the above (c) Higher utility level
4. Suppose that good 1 and good 2 are perfect complements for Andy and that he always consumes 2 units good 1 for every 3 units of good 2. 1 (a) Sketch few indifference curves for Andy. (b) Find Andy's Marshallian demand (utility maximizing bundle). (c) Show whether good 2 is inferior. (d) Show whether good 2 is Giffen.
(D)
12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.
4. Tim wants to maximise his utility given his utility function of U(A, B) = A²B4. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA = 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income