Consumer has utility function In(c1)+beta*In(c2), where beta=1. Interest rate i=0%. (NOTE!) Income y1=10 and y2=50. Gov't gives consumer a free stimulus check of $20 in the first period.
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- Consider an economy in which there is one consumer born at the start of each time period. Each consumer lives for two periods and receives an endowment of 1 unit of the consumption good when young. At the start of the economy there is a consumer who is already old. This consumer owns one unit of money but has no endowment of the consumption good. Money has no intrinsic value. a. Can money be valuable in a finite economy (one that has a known end point)? b. Can money be valuable in an infinite economy? c. Can money allow exigency to be attained?Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…Josh is playing blackjack for real money. He has reference-dependent preferences over money: if his earnings are m and his reference point is r, then his utility is v(m − r), where the value function v satisfies v(x) = ln(x + 1) for x ≥ 0, and v(x) = −2 ln(−x + 1) for x ≤ 0. assume that Josh’s reference point is 0 Euro (that is, no wins or losses) and for the given situation, answer the following questions: (i) What is the g for which Josh would be indifferent between taking a fifty-fifty win g Euro or lose 5 Euro gamble? (ii) Does this reflect risk loving or risk averse behavior? (iii) What feature of Josh’s reference-dependent preferences is driving this choice?
- What is meant by “excess sensitivity” of consumption? Is this view of consumption consistent with the permanent-income hypothesis? Explain. How does the stock market affect consumption according to the permanent-income hypothesis? Is this prediction in line with the empirical evidence? Explain.According to the basic discounting principle, individuals value current consumption (i.e. consumption now) more than future consumption (i.e. consumption tomorrow). A) True B) FalseKevin's reference dependent utility over money is y and effort is E, refer to the: instantaneous utility function: rt: reference point for wealth, which demonstrated his recent wealth Kevin does not have from money but from gains and losses of money instead. There is no discounting, and assume that Kevin's current wealth from his job is 0. Kevin is thinking about a new role at work which allows him to increase his income by $1000 per period for two periods, counting from the current period, which is t = 0. He must undergo a training which require an effort of EO = 3500 at that value of alpha, how much ultility would Kevin lose relative to his non-projection-biased preferences if she took the position 1000 250 500 750
- We consider a two-periodendowmenteconomy. Suppose you have the following utility function U （c , c ′）=lnc +βlnc ′ where c and c ′ refer to consumption in the first and second periods, respectively, and β =0.5. The household income in the first and second periods is denoted by y and y ′. Assumegovernment collects lump-sum tax in both periods (T, T ′)to finance the public spending inboth periods (G , G ′)and issue bonds B in the first period. A real net interest rate r is 1. 1. Write down the household’s problem. Does the household perfectly smooth their con-sumption over lifetime? Show it using the optimality condition. 2. Solve for optimal c , c ′ and s (saving) when y −T > y ′−T ′. 3. Given the conditions in part (2), there is an increase in future income y ′ such that y −T =y ′−T ′. Find new optimal c , c ′ and s . Explain how c , c ′ and s change compared to part(2). 4. Focusing on part (3),(a) Suppose that the government increases T by a small amount and decreases T ′ bythe…In the two-period Fisher model of consumption, suppose that the first period income is $5,000 and the second period income is $5,000 for both Matt and Paola. The interest rate is 10 percent. Matt’s lifetime utility function is C1 + C2 while Paola’s lifetime utility function is C1 + 0.8C2. If there is a borrowing constraint, whose consumption is affected by that?Consider the two-period endowment economy we discussed in class. In this economy, a household lives for two periods and can save s. The return on saving is the real interest rate,r. Income is exogenous and given as y and y'. Households have utility overconsumption,c, in each period by U(c)=In(c)+B In(c') where future utility is discounted with rate B. Households choose consumption in both periods,c and c'. 1-Write down the current period and future period budget constraints. Derive the lifetime budget constraints. 2-What is the slope of the lifetime budget constraint? What are the intercepts? What is the significance of the endowment point? 3-Write down the expression for the consumer's optimization problem. What is the tangency condition? Provide an intuitive explanation for this condition. 4-Solve for c,c', and s. Given that B=1 and r=0, how would you modify the answers for c,c; and s? Explain.
- Suppose that the economy of country 1 is characterized by the following behavioral equations: Variable Equation Consumption C=1234 +0.5 YD Investments I=1000 + 0.1 Y Government expenditures G= 100 Net exports Nx= 300-0.2 Y Where Y denotes the real GDP and YD denotes the disposable income (YD= Y-T). Suppose that the output gap in country is measured as -15000. What should be increase in government expenditure in order to close the gap and make the economy to reach its potential level of GDP?.Q) Assume consumers with standard preferences live for two periods. They receive an income in each period (? and ?′) and pay lump-sum taxes to the government (? and ?′). Credit markets are not perfect, and borrowers are charged a higher interest rate than lenders. The government never defaults, and faces the lenders’ interest rate whether it borrows or lends. Which are true? a) The number of lenders is equal to the number of borrowers b) A reduction in taxes in the current period without changes in the lifetime burden of taxes increases current consumption for a lender c) A borrower is better off if there is a reduction in the interest rate paid by borrowers d) A borrower is better off if there is a reduction in the interest rate paid by borrowers, but only if the substitution effect dominates the income effect e) A reduction in taxes in the current period without changes in the lifetime burden of taxes may transform a borrower into a lenderConsider a finance economy with two states with probabilities pi1=1/3 pi2=2/3. Both agents have utility of income v(w)=ln(w). Current consumption does not enter agents expected utilities; they are interested only in consumption tomorrow. The agents receive endowments of wealth tomorrow. In state 1 agent A will get 6 units of wealth, in state 2 he will receive 3 units. Agent B will get 6 units of wealth in both both/either state. - Compute the equilibrium prices of wealth, (Arrow security prices), and the equilibrium allocations of wealth for Agents A and B... Hint:you need to set up the optimisation problem for each agent, solve for the demands for contingent wealth, impose market clearing conditions and solve for the equilibrium prices of wealth in different states (or their ratio).