4. Consider the above two-periods endowment economy. Suppose there are identical agents but with different endowments. There are a number of L₁ Type 1 agents with endowments Y (1) = 1, Yt+1(1) = 0, and a number of L₂ type 2 agents with endowments Y (2) = 0, Yt+1(2) = 1. Then a. At time t, type 1 agent has more consumption than type 2 agent b. At time t, type 2 agent has more consumption than type 1 agent c. Since this is an endowment economy, saving must be zero: type 1 agent will have 0 consumption at t+1 d. The equilibrium interest depends on individual income heterogeneity

4. Consider the above two-periods endowment economy. Suppose there are identical agents but with different endowments. There are a number of L₁ Type 1 agents with endowments Y (1) = 1, Yt+1(1) = 0, and a number of L₂ type 2 agents with endowments Y (2) = 0, Yt+1(2) = 1. Then a. At time t, type 1 agent has more consumption than type 2 agent b. At time t, type 2 agent has more consumption than type 1 agent c. Since this is an endowment economy, saving must be zero: type 1 agent will have 0 consumption at t+1 d. The equilibrium interest depends on individual income heterogeneity

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fast
Alex preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?
James's preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?
Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%.(i) Draw and carefully label the merchant’s endowment point, their expected income, and their certainty equivalent income in a 2-dimensional state-contingent consumption space. Use the diagram to illustrate and explain how the merchant would benefit from buying insurancein a competitive insurance market. At which point a risk-neutral insurance firm would maximisetheir profits by offering the merchant full insurance?
Households live two periods and have prefernces U(c1)+βU(c2) where 0<β<1 and U is the utility function and satisfies our usual assumptions. There are N households in the economy. N1 of these have endowments y1 in the first period and no endowment in the second-these agents are called "Type 1". The remaining N2 have no endowment in the firs period and y2 in the second period- these agents are called "Type 2". Hencethe resources of the economy are N1y1 in the first period and N2y2 in the second, where N=N1+N2 Households have access to a credit market where the can borrow (s<0) or save s<0. The type 1 agent faces budget constraints y1=c11+s1 rs1=c21 where the consumption for the type i agent in period j is denoted cji. The type 2 agent faces budget constraints 0=c12+s2 y2+rs2=c22 The resource constraints are N1y1=N1c11+N2c12 N2y2=N11c21+N2c22 a) state the maximization problem solved by each type of agent and derive the fist order and second order conditions. Derive the…
H3. An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 − C0)0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0, C1) =C0C1 . What is the NPV of the investment chosen by the investor? Show proper step by step calculation
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Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. (i) Draw and carefully label the merchant’s endowment point, their expected income, and their cer- tainty equivalent income in a 2-dimensional state-contingent consumption space. (ii) Use the diagram to illustrate and explain how the merchant would benefit from buying insurance in a competitive insurance market. At which point a risk-neutral insurance firm would maximise their profits by offering the merchant full insurance?
Constructing an equilibrium Households live two periods and have prefernces U(c1)+βU(c2) where 0<β<1 and U is the utility function and satisfies our usual assumptions. There are N households in the economy. N1 of these have endowments y1 in the first period and no endowment in the second-these agents are called "Type 1". The remaining N2 have no endowment in the firs period and y2 in the second period- these agents are called "Type 2". Hencethe resources of the economy are N1y1 in the first period and N2y2 in the second, where N=N1+N2 Households have access to a credit market where the can borrow (s<0) or save s<0. The type 1 agent faces budget constraints y1=c11+s1 rs1=c21 where the consumption for the type i agent in period j is denoted cji. The type 2 agent faces budget constraints 0=c12+s2 y2+rs2=c22 The resource constraints are N1y1=N1c11+N2c12 N2y2=N11c21+N2c22 a) state the maximization problem solved by each type of agent and derive the fist order and second order…
1- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Select one: True False 2-Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Select one: True False 3-A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Select one: True False 4-If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Select one: True False
Let W0 represents an individual’s current wealth and U(W) is this individual’s von Neumann-Morgenstern utility index (or utility function) that reflects how s/he feels about various levels of wealth. Assume this individual marginal utility of wealth decreases a wealth increases. Which of the following statements is true? a. This individual will prefer to keep his or her current wealth rather than taking a fair gamble. b. For this individual, a 50-50 chance of winning or losing c dollars yields less expected utility than does refusing the bet. c. This individual is said to be risk averse. d. All of the above.
Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???