(c) Consider a two-period small open endowment-economy populated by a large number of identical households with preferences described by the lifetime utility function (C1)°¹ (C2)2, where C1 and C2 denote consumption in periods 1 and 2, and a₁ and a2 are the weights on consumption. Suppose that households receive exogenous endowments of goods given by Q₁ = 10 and Q2 11 in periods 1 and 2. Every household enters period 1 with some debt (B) inherited from the past. Let B be equal to -5. The interest rate on these liabilities, denoted ro, is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r*, is 10 percent. 1. Calculate the value of the household's lifetime wealth, Y. 2. Assume that a₁ =a2. Compute the equilibrium levels of consumption in periods 1 and 2. 3. Now, compute the equilibrium levels of the trade balance and the current account in period 1. 4. Assume now that the endowment in period 2 is expected to increase from 11 to 16.5. Calculate the effect of this anticipated output increase on consumption in periods 1 and 2, the trade balance in period 1, and the current account in period 1. Provide intuition.

(c) Consider a two-period small open endowment-economy populated by a large number of identical households with preferences described by the lifetime utility function (C1)°¹ (C2)2, where C1 and C2 denote consumption in periods 1 and 2, and a₁ and a2 are the weights on consumption. Suppose that households receive exogenous endowments of goods given by Q₁ = 10 and Q2 11 in periods 1 and 2. Every household enters period 1 with some debt (B) inherited from the past. Let B be equal to -5. The interest rate on these liabilities, denoted ro, is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r*, is 10 percent. 1. Calculate the value of the household's lifetime wealth, Y. 2. Assume that a₁ =a2. Compute the equilibrium levels of consumption in periods 1 and 2. 3. Now, compute the equilibrium levels of the trade balance and the current account in period 1. 4. Assume now that the endowment in period 2 is expected to increase from 11 to 16.5. Calculate the effect of this anticipated output increase on consumption in periods 1 and 2, the trade balance in period 1, and the current account in period 1. Provide intuition.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

See similar textbooks

Similar questions

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…
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…
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?
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?
Q. 5. For auto makers, an important decision is to determine what features a new car model should be provided based on cost-benefit analysis. In what ways can economists help auto manu- facturers estimate the marginal rate of substitution between features such as vehicle interior size and acceleration? (a) Examining production cost data (b) Conducting consumer surveys about willingness to pay for auto features (c) Solving the standard consumer model (d) Statistically analyzing historical data on purchases of different types of autos (e) B and D only Q. 10. When firms determine whether to invest in research and development (R&D), they need to consider many factors. Which of the following is NOT one of the important factors that should be considered? (a) The market size of the product today. (b) The market potential for the product in the next few years. (c) The R&D investment of the competitors on similar products. (d) Potential new products that may be substitutes of the…
Consider the two-period model in partialequilibrium, i.e. the endowment economy. Assume that there is a decrease in technology such that the endowment in the first period decreases (relative to standard level, say) but the endowment in the future remains unaffected. Explain graphically and in words the effects of this change on the optimal intertemporal allocation of consumption, assuming that without the endowment change the consumer would have been a lender in the first period. Explain the effects of this change on the intertemporal prices, Disentangle the effects of the overall change in endowment between income and substitution effects.
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. Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? B. Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. C. In this particular example, what are the contributions of the income and substitution effects?
"Companies should use investment entry modes whenever possible because they offer the greatest control over business operations." Do you agree or disagree with this statement? Are there times when other market entry modes offer greater control? How (if at all) do you think a company's product influences the choice of entry mode? Cite the example of 2 products that would influence the choice of entry mode in a different way.
Need help on part (d) and (e) 6. 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. a) 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). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply decreases.…
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.
Consider a representative consumer with preferences over consumption e and leisure I given by u(e,l) = 1/4 * ln(c) + 3/4 * ln(l) Assume that the price of consumption is normalized to p = 1 and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 24 The consumer also receives dividend (profit) income of pi = 39 and pays lump-sum taxes of T = 7 (a) Write out the consumer's budget equation, and draw a graph of the budget constraint. (b) Solve for the optimal decisions e and 1. How many hours per day is the consumer working? (c) Suppose the consumer's wage decreases to w = 16 Solve for the new optimal choices of c and I". Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the wage changes in part e, determine whether the consumer experiences an income effect, a substitution…
In a typical product mix model, where a companymust decide how much of each product to produceto maximize profit, there are sometimes customerdemands for the products. We used upper-boundconstraints for these: Don’t produce more than youcan sell. Would it be realistic to have lower-boundconstraints instead: Produce at least as much as isdemanded? Would it be realistic to have both (wherethe upper bounds are greater than the lower bounds)?Would it be realistic to have equality constraints:Produce exactly what is demanded?