2. Consider a consumer with preferences over current and future consumption given by U(C₁, C₂) = (c₁)¹/2 (c₂)¹/2 where c₁ denotes the amount consumed in period 1 and c₂ the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m₁ = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p₁ = P2 = 1 and let r denote the interest rate. (a) Find the optimal consumption bundle when r = 0.15. Is the consumer a saver or a borrower?

2. Consider a consumer with preferences over current and future consumption given by U(C₁, C₂) = (c₁)¹/2 (c₂)¹/2 where c₁ denotes the amount consumed in period 1 and c₂ the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m₁ = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p₁ = P2 = 1 and let r denote the interest rate. (a) Find the optimal consumption bundle when r = 0.15. Is the consumer a saver or a borrower?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider a two-period consumption saving model and let ci and c2 denote the first and second period consumption, respectively. Assume that the interest rate at which the consumer may lend or borrow is 10%. Suppose that a consumer's utility function is u (C1, c2) = c1 + 20 c2. The consumer first period income is I1 = $100 and the present value of her income stream is $330. (a) What is the optimal consumption stream (consumption bundle) of this consumer? (b) Is this consumer borrower or lender? How much does she borrow or lend? (c) What is the effect of a reduction of the interest rate to 5% on the consumer's optimal first-period saving? (Make sure to take into account the effect of the decline in the interest rate on the present value of the consumer's income stream.)
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.
3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
A consumer's ordinary demand curve for x1* (p1, p2, 1) = [² p1². How will a 2% increase in income affect this consumer's consumption of x1? O 1% 2% 3% 4% 5%
1. Consider a two-period model in which you work and save in the initial period (period 0) and live off savings and the interest from savings in retirement (period 1). Suppose that income in period 0 is $250,000, income in period 1 is $0, and the interest rate is 50%. a. Draw the budget line. b. Draw an indifference curve consistent with a person whose preferences causes them to equalize their consumption in period 0 and period 1. c. Savings are $_ d. Draw the after-tax budget line if a personal income tax is introduced with a marginal tax rate of t= 40%. e. Suppose that preferences are such that after tax consumption is equalized in period 0 and period 1. On the diagram show after-tax savings. Сі ($x 1,000) 450 400 350 300 250 200 150 100 50 25 50 75 100 125 150 175 200 225 250 275 300 325 350 Со ($ x 1,000)
Economics Michelle is a saver, and consumption in period 1 is a normal good. If there is an increase in the interest rate: Group of answer choices Both the substitution and income effects will decrease consumption in period 1. Cannot be determined without additional information. The substitution effect will increase consumption in period 1, whereas the income effect will decrease it. Both the substitution and income effects will increase consumption in period 1. The substitution effect will decrease consumption in period 1, whereas the income effect will increase it.
13. Suppose that AS = 3SAT + 2SAX and that today's price is S(0) = 50. Find (i.e., derive) the PDF for the price of S(1), the price one year from now.
Thank you for your solutions of questions 1-3. Please answer questions 4-5.