Is the competitive equilibrium of this economy Pareto optimal? If yes or no, explain why.Yes. The first welfare theorem ensures the Pareto optimality of the competitive equilibrium.No. Because in this economy, MRS₁¸c < MRT₁¸c holds, which violates the Pareto optimalitycondition.No. Because in this economy, MRS₁,c > MRT₁,c holds, which violates the Pareto optimalitycondition.Neither yes nor no. We need more information to determine whether the competitiveequilibrium is Pareto efficient. Consider the decisions of a representative consumer whose preferences are given by:u(C,1) = In C+ Inlwhere C is the quantity of consumption and 1 is the quantity of leisure.The consumer faces two constraints.The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the laborsupply). Further, consumer take wages as given and obtain after-tax labor income that is equal tow(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint isgiven byC = w(1 − t)(1 − 1) + πwhere is the real dividend income received from the representative firm (i.e. firm profits).

Taking into account the preferences of the representative consumer, we must evaluate whether…

Answered: Is the competitive equilibrium of this…

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 the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).
Consider a utility function defined over hours of leisure and consumption expenditure: U(c, h) ch. The after- tax wage rate is given by w and the amount of nonwage income, by N. Assume the number of hours of leisure in a year is 8000. Potential annual income, I, is given by 1-8000wN. It is allocated over hours of leisure, which cost wh, and consumption expenditure, c. The budget constraint is thus 8000wN-cwh 0. 1. Find the demand functions for leisure and consumption. a. Write the Lagrangean function for this problem. b. Find the first order conditions. c. Solve the first order conditions to obtain the condition that the MRS wage rate. Show your steps in the solution. d. Use the results from c to obtain the expansion path
5. Consider a representative household in the static consumption-leisure model with prefer- ences given by u(c, 1) = Ac¹/² +1¹/2. The household has a unit time endowment given by 1 = 1+n, faces a price of P on consumption, and earns nominal wages at rate W on their labor supply, n. In addition, the household faces a proportional tax on wage income of T. (a) Interpret in words the economic significance of the exogenous parameter A. (b) Interpret in words the economic significance the unitary time endowment.
An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?
Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.-→0 u'(c) approaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount c2 is financed out of the…
Rodrigo is taking a year between high school and college to work and save up. His utility from consumption each year is U(c) = discounts future utility by B. Rodrigo is going to make $I his year of working, and whatever he doesn't consume from that income will a savings account which will earn return r before he consumes next year. He has to pay for school expenses E in year two, before he consumes (but after return has been realized). 1-o and he go into
Define time preferences for consumption
3) Marco has $100 worth of grain in period 1 but gets no grain in period 2. Marco has two choices. He can store the grain that he does not consume in period 1. This results in a loss of 20% of the grain due to pests. Assume that with this option he will choose to consume 68 units of grain in period 1 and 26 units in period 2. Instead, Marco can sell the grain he does not consume in period 1 and lend the money from that sale to someone today at an interest rate of 10%. He can then use the repayment of that loan to buy gain in period 2. a) Based on this information, draw a diagram that outlines Marco's choices. Is he definitely better off once the opportunity to lend is available to him? b) Relative to his initial equilibrium point, does he unambiguously consume more in both periods once he can lend out the excess he does not consume in period 1? c) Now assume that Marco can sell any excess grain he doesn't consume in period 1 and invest the money he gets in a new type of risky activity.…
Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes).
Antonio is a researcher who teaches thermodynamics at a university where he earns an annual salary of $160,000. He intends to take the next year off to focus on writing a new undergraduate physics textbook, so he will not earn any income next year. He is currently deciding how much of this year's salary he should save for next year. Assume that there are no tax implications associated with the decision, and ignore what happens after next year. Therefore, next year Antonio will consume whatever he saves this year plus interest, and he is not concerned with the future beyond next year. The following graph shows Antonio's preferences for consumption this year and next year. Suppose initially Antonio cannot earn interest on the money he saves. Use the green line (triangle symbol) to plot Antonio's budget constraint (BC₁) on the following graph. Then use the black point (plus symbol) to show his optimum consumption bundle. Note: Dashed drop lines will automatically extend to both axes.…
I Consider a consumer who has the following utility function of consumption ( C 1. -- ) and leisure ( L ), U = CL?. The wage rate is $20 per hour, the price of consumption is $10 per unit, and the consumer's non-labor income is $60. The time endowment of the consumer is 24 hours. (1).( ) What's the utility-maximizing choice of consumption and leisure? (2).( Show that at that choice, the marginal rate of substitution between consumption and leisure is equal to the real wage.
Say you define your permanent income as the average income this and the past 4 years’ incomes and you always consume 4/5 of your permanent income. Your earnings record over these years has been: Yt = 40,000 Yt-1 = 38,000 Yt-2 = 34,000 Yt-3 = 32,000 Yt-4 = 31,000 If next year your income increases to Yt+1 = 46,000 by how much will your consumption change between year t and year t+1?

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