7. [5 points] Let a consumer's utility function be U(x, y) = VVg. The consumer's income is I = 3, 200 and prices for the two goods are, respectively, p = 2 and p, = 8. %3D (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose the price of good y decreases to p, = 2. Compute the new optimal consumption basket. (c) Compute and represent graphically the substitution, income and total (price) effects. Is good y ordinary or Giffen for the consumer, and why?

7. [5 points] Let a consumer's utility function be U(x, y) = VVg. The consumer's income is I = 3, 200 and prices for the two goods are, respectively, p = 2 and p, = 8. %3D (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose the price of good y decreases to p, = 2. Compute the new optimal consumption basket. (c) Compute and represent graphically the substitution, income and total (price) effects. Is good y ordinary or Giffen for the consumer, and why?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Questions 4 (Choice & Demand). Suppose a consumer's utility function is given by: U(xi, x2 ) = x" a) What is the consumer's demand for x, as a function of income and prices? What is the consumer's demand for x; as a function of income and prices? Use Lagrange method or your intuition. b) What percentage of income does the consumer spend on x;? What percentage of income does the consumer spend on x2?
2) A consumer of two goods, either 1 or 2, has a utility function U (X1, X2) = x1 0,6.x2 0.4, where x denotes units of good 1 and x2 units of good 2. The price of good 1 is 5 euros per unit, the price of good 2 is 3 euros per unit and the consumer's income is 150 euros. Suppose only the price of good 1 changes and so does the new one price is p1‘ = 2. Then the Slutsky substitution effect with respect to good 1 is Choose one: A) Not defined B) 10.8 C) 8.8 D) 7.8 E) 9.8
3. [30+10] A consumer who consumes two goods and has the following utility function: U(x₁, x₂) = log(x₁ + 1) + log(x2 + 1), where ₁ and ₂ denote the monthly consumption of two goods. The consumer maximizes her utility subject to the following constraints: P₁x1 + P₂x2 ≤m, x₁ ≥ 0, X₂ ≥ 0, where p₁ > 0, p2 > 0 and m > 0. [Hint: Note that log f(x) = f(df (2).] 1_df f(x) dx (a) Write down the Kuhn-Tucker conditions for a point (x₁, x2) to solve the problem, and find all points that satisfy the conditions. Do any of those points solve the problem? (b) Show the above results by drawing indifference curves and budget set on the x₁x2 plane.
5. Suppose the representative consumer has the (quasilinear) utility function: U(x, y) = ax + In(v) where x,y are consumption goods. Denominated in US dollars, the prices of x and y Pi and pz, respectively. (a) What does the term quasilinear mean? Is consumption of x independent of y? (b) Assume the consumer has a budget of C dollars at his/her disposal. What is the maximum utility the consumer may achieve with this budget? (c) What is the minimum expenditure if the consumer wants to derive U,units of utility?
3. Suppose Product X is a normal good and its price (Px) decreases. Graphically illustrate its Substitution and Income Effects using individual's budget and indifference curves
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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.
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
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
5) A consumer of two goods, good 1 and good 2, has a utility function u (X1, X2) = x1 0,6. X2 0,4, where x denotes units of good 1 and X2 units of good 2. The price of good 1 is 5 euros And the price of good 2 is 3 euros per unit and the consumer’s income is 150 euros. Suppose that only the price of good 1 changes and that the new price is p, ‘ = 2. Then the demand function of good 1 that is derived from the utility function is Choose one: A) X1= 0.6m/p1 B) X1= 6m/p1 C) X1= 4m/p1 D) X1= 0.4m/p1 E) Not defined
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4- An indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. Food Clothing a) Danyal is obsessed with food and clothes. Assume you have no knowledge of the budget line, what point would Danyal prefer to be at. b) Why can't two indifference curves not intersect, explain and illustrate your answer. c) As we move from point c to f, who's marginal rate of substitution declines.