1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form $ U(c_1, c_2) = c_1^{\frac{1}{2}} c_2^{\frac{1}{2}} $. The general form of the slope of the indifference curve for the representative consumer is $ -c_2/c_1 $. Moreover, remember that $ c_1 = y_1 - s $ and $ c_2 = y_2 + s(1 + r) $.a. Assume that the representative consumer has an endowment of consumption goods in the two periods of $ y_1 = 20 $ and $ y_2 = 10 $. Assuming an interest rate $ r = 1 $, compute the equilibrium allocation and the implied savings.b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that $ y_2 = 0 $. What happens to the savings $ s $ in the first period?c. In the previous part, the interest rate remained at 1. Now, consider the savings function, that is, the relationship between the real rate of interest and the amount saved. The equilibrium interest rate is then determined as a market price in the Saving-Investment diagram.Given the typical shape of the investment curve, what would happen in response to the rate of interest in response to an attack of pessimism? Would the change in price (the interest rate) amplify or reduce the magnitude of the shock to the quantity of savings? Explain with the help of a graph.

Utility function : U = c10.5 c20.5 In period 1 - Budget Constraint : c1 + S = y1 In period 2 -…

1. Suppose that the representative consumer has a utility function defined over 11 consumption over two dates of the form U(C₁, C₂) = C₁zc₂2. The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = Y₁ - S and C₂ = y₂ + s(1 + r). Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in

1. Suppose that the representative consumer has a utility function defined over 11 consumption over two dates of the form U(C₁, C₂) = C₁zc₂2. The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = Y₁ - S and C₂ = y₂ + s(1 + r). Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Steve's utility for socks (q1) and other goods (q2) is given by U(q1,q2) = 10q10.1 0.1q² 0.9 The price of the composite good is p2=1 and the price of a pair of socks is p1=2. Steve's income is Y=100. Every year, Steve's mom buys him 20 pairs of socks. How many dollars is the equivalent variation of the $40 that his mom spends on socks every year?
2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?
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Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u(xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po (a) (b) Write down Anne's budget constraint and utility maximization problem, and the Lagrangian associated with this utility maximization problem. Find Anne's Marshallian demand functions for apples and oranges. Find Anne's indirect utility function.
Please draw the income-consumption (or income-offer) curve for each of the following utility functions, indicating the slope of each: (a) U = (A)(x^a)(y^b) (b) U = min(ax, by) (c) U = ax + by
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
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