2. Consider an economy consists of three types of economic agents who live for two periods. Their utililtyfunction is given byu (c1, c2) = loge + ß log owhere 3 € (0, 1). Workers differ by their income stream, which is exogenous.(type-X 1=2 and y2=2type-Y y1=4 and y2=0type-Z 1=0 and y=4There is a capital market with interest rate r =(a) Solve for the optimal consumption of each type. What is the ratio between c1 and ez? Does thisratio differ by type? Explain.(b) Compare the optimal consumption level of each type. Who consumes the most? Provide economicinterpretation of your results.(c) Suppose the government imposes capital taxes TK > 0. Find the equilibrium consumption (č1,č2) for type-X. Does your answer differ from the previous results in (a) and (b)? Why or whynot?

Utility refers to the total amount of satisfaction derived by an individual after consumption of a…

Answered: 2. Consider an economy consists of…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a one period model in which a representative agent maximises the utility function: u(c,l) = lnc + 5lnl subject to the budget constraints: c = (1-t)w(1-l) + v where c is consumption and l is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. A. Solve for first order conditions of the representative agent. B. Write down the market clearing condition (resource constraint) for the aggregate economy. C. Solve for equilibrium consumption and labour choices.
Person 1 and person 2 are the only two residents of an economy. Person i (where i is either 1 or 2) has the utility function Here, Yi is person i’s income and β is parameter between 0 and 1. Assume that the social welfare function is where α is a parameter between 0 and 1. Initially, person 1’s income is 1 and person 2’s income is 2. a) Express W in terms of Y1 and Y2. If a social indifference curve shows all the pairs (Y1, Y2) that yield the same value of W, what would a social indifference curve look like if it were drawn in the (Y1, Y2) quadrant? Find an algebraic expression for the slope of a social indifference curve. b) Imagine that income redistribution is costless, in the sense that the economy can reach any pair (Y1, Y2) that satisfies the condition Draw a graph of the attainable pairs in the (Y1, Y2) quadrant. This set is called the “utility possibility frontier.” Using this frontier and the social indifference curves,…
Consider a random-relocation economy where each young person receives 10 units of the consumption good. There are 100 young people born each period. The total stock of money is constant and equal to $500. The consumption good can be transformed, one to one, into capital, which will give a return of x > 1 next period. Suppose a personís preferences are such that they want to consume 1/2 of their endowment when young 2 of ECON20532 and 1/2 when old. They all dislike risk. We also assume that the probability that a person is relocated is 10% (known to everybody) and the gross return on capital is 1.1. A person is notifed whether she needs to relocate or not at the end of period 1. A person who relocates can take with her money, but not capital. Individual agents cannot invest directly in capital, but there exists a (perfectly competitive) banking sector that accepts deposits from all young people. (a) What is the state contingent rate of return o§ered by banks on deposits? (b) Write…
2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has T hours each day which can be allocated toward working time, H, or leisure time, L-that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money. (1) Formulate the individual's problem as an optimization problem with two constraints a time constraint and a money constraint. Derive the first-order conditions. Give an economic interpretation of the Lagrange multipliers. (2) The two-constraints problem can be…
The COVID pandemic has changed where many people are able to do their work at the city or metro-area level. Which of the following best describes the predictions from a Rosen-Roback style model on how separating work (in the model, wage) from location of residence might impact house prices across different areas. O This should put upward pressure on house prices (and population) in traditionally high-wage areas, and downward pressure on house prices (and population) in traditionally high amenity areas. O This should put downward pressure on house prices (and population) in traditionally high-wage areas, and upward pressure on house prices (and population) in traditionally high amenity areas. O This should put upward pressure on house prices across all areas, regardless of the initial factors associated with that area. O This should put downward pressure on house prices across all areas, regardless of the initial factors associated with that area.
Consider an Edgeworth box economy where preferences are given by u'lx},x3) = x} + Inx and uaf,x3) = xi, and the initial endowments are e' = (1,3) and e² = (3,1). Find all the Walrasian equilibrium. You may assume that the solution is inte- rior.
8
The most general form of a social welfare function (SWF ) can be written as W = W(U1; ... ; UH). a. Explain the following properties that a SWF may satisfy: non paternalism, Pareto principle, anonymity (the names of the agents do not matter), and concavity (aversion to inequality). b. Consider two agents h = 1; 2 with utilities U1 and U2. Depict the social indifference curve of the utilitarian SWF in (U1; U2)-space. Which of the properties in part a does it satisfy? c. Depict the social indifference curves of the maxim in or Rawlins SWF. Contrast to the utilitarian SWF with respect to the aversion to inequality. Which properties does the Rawlins SWF satisfy? d. The Bernoulli-Nash social welfare function is given by the product of individual utilities. Discuss the distributional properties of the Bernoulli-Nash SWF.
This problem considers the decisions of a consumer whose preferences are given by u(C, 1) = C + y log 1, in which is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N = 1 with N³ as the time spent working (or the labor supply). Assume that 0 < x < 1. The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to w Nº. The budget constraint is C = wN+T-T, with as real dividend income and T as the real lump-sum taxes paid to government. Assume that an interior solution always exists in the optimal consumption-leisure choice.
An economy with competitive markets has 2 kinds of jobs, Routine & Skilled. There are 2 types of workers, Qualified & Unqualified. 60% of workers are Qualified while 40% are unqualified. In a Routine job, both types of workers produce 10 widgets. In a Skilled job, Qualified workers produce 100 widgets each, while Unqualified workers produce 0. Labor markets are competitive, so each worker is paid their marginal product, i.e. how much they produce, in widgets. Everyone looks great in an interview, so companies must hire without knowing the worker's type and must pay the first period's wage without knowing their actual output. However, Qualified workers can signal their qualification by receiving an education. For a Qualified worker, the cost of getting educated to level n is 0.5n2. For an Unqualified worker, it is n?. These costs are also measured in widgets. What is the maximum level of education that Qualified workers will obtain, in a separating equilibrium? O 13.5 O 12 O 13 O 10
Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x, M) = 2 ln x + ln M. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). =
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