In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where C₁, C₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers are identical. ** Part a

In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where C₁, C₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers are identical. ** Part a

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q. 1
Consider a two-period endowment economy with a single representative agent. That agent's utility function is: U = In(ct) + (1/2)In(Ct+1) In this endowment economy, output is 100 in period t and 150 in period t+1. What is the equilibrium interest rate (r) in this economy? Write your answer as a percentage, but omit the percent sign. So if you think r=0.1, that's 10%, but write 10. Similarly, if you think r = 1.5, that's 150%, but write 150.
answer only question 1
Given the significant increases in the cost of living in Canada (and elsewhere), Governments (both Federal and Provincial) have been under pressure to provide financial support to at last individuals or households. This financial support can be in the form of direct payments (income) to individuals or subsidizing the purchase of certain goods (i.e. the government pays a portion of the purchase price). To keep things simple, let’s only consider our standard example in which the individual consumes food and clothing; and food is the good whose purchase is to be subsidized. a) Evaluate the impact of both of these options on the utility of the individuals receiving support. (40%) b) Suppose the government only subsidizes the purchase of the first 5 units of food, how does this change your answer to a)? (40%) c) If the government ends up spending the same amount of total subsidies in either case (income support or price subsidy), which option will have a more substantial effect on the…
Assume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours? b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours. c. What is this individual’s optimal amount of consumption and leisure?
question C Please
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Consider a one-period model in which the representative consumer splits 100 hours of available time between work hours denoted by NS and leisure hours denoted by L. The consumer receives wage rate w = 9 for every hour worked. In addition, the consumer receives dividend income = 29 and pays lump-sum taxes T = 81. Derive the budget constraint of the consumer. Type in the appropriate numerical values in the boxes provided below to obtain the equation that defines the budget constraint of the consumer. All numerical values should be integers, hence use 0 decimal places. The budget constraint is C = -XL, where the symbol x denotes a multiplication sign.
For example, the economy of a country can be explained by several models as follows: Consumer: The consumer derives his satisfaction from his current consumption, future consumption and his free time (u(C,C',l,l'). He maximizes his utility by: C+wl+11+rC'+w'1+rl'=wh+π-T+w'h+'-T'1+r It is assumed that consumer preferences meet the general conditions that are often used (more is better, preference for diversity, all goods are normal, substitution effect is more dominant). Firm: In the first period, the firm has K capital and employs N workers to produce Y output: Y outputs: Y=zF(K,N) The profit in the first period is =Y-wN-I Where I is the company's investment. Investments increase the capital stock for the second period: K'=1-dK+I In the second period the firm will produce output of Y': Y'=z'F(K',N') Then the profits obtained in the second period are: '=Y'-w'N' Firms choose the demand for labor (N, N') and the demand for investment I to maximize their value: V=π+π'1-r…
Consider the household model that you have seen in class but now assume that the goal of the household is to consume twice as much in period 2 as in period 1. She earns $100 in the first period and $150 in the second period. The interest rate is 5%. What is her optimal saving in the first period? Note: Type in your answer approximated to two decimal points, i.e., your answer must be of the form "999.99". I will not be able to fix correct answers that were entered incorrectly, such as "999.999" or "999,99" or "999". In case the last digit in the correct answer is zero, e.g., "999.90" or "999.00", Blackboard will automatically delete it and you should not do anything about it.
Q2: Let a consumer’s daily hours of work is denoted by H, and hours of leisure by L. Consumer has no other source of income except wages for hours worked. She consumes what she earns each day. Her utility function is U(C, N) = ln(C) + 3 ln(N) Where C stands for the dollar amount of her consumption. Now answer following questions (a) Suppose the wage rate is 50Rs. per hour. Write down the consumer’s utility function and budget constraint with C and H as the choice variables. (b) How many hours will she choose to work, and what will be the resulting utility?
Suppose we wanted to investigate the saving and borrowing behavior of consumers. It’s not that difficult to extend our basic model. We can use the same framework as before, but define our two goods as “consumption in period 1” (horizontal axis) and “consumption in period 2” (vertical axis). a. Construct a budget constraint for a consumer who earns $100 in income in period 1 and $300 of income in period 2. Label this point E for the “Endowment” point. Assume that he can choose to save some income in period 1 to be used in period 2, or to borrow some income from period 2 to use in period 1. (Let’s imagine the consumer saves the money by putting it in a piggy bank and can borrow money from his parents, who don’t charge interest.)