4. Consider a two period model with investment Imagine a preference shock that increases the representative consumer's utility for leisure. Therefore, the consumer chooses to consume more current leisure and less current consumption, and more future leisure and less future consumption. (everything else is equal) given the initial real interest rate r; a) What effect this preference shock has on labor supply curve? b) What effect this preference shock has on labor demand curve? c) What effect this preference shock has on output supply curve?
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4.
Consider a two period model with investment
Imagine a preference shock that increases the representative consumer's utility for leisure. Therefore, the consumer chooses to consume more current leisure and less current consumption, and more future leisure and less future consumption. (everything else is equal) given the initial real interest rate r;
a) What effect this preference shock has on labor supply curve?
b) What effect this preference shock has on labor demand curve?
c) What effect this preference shock has on output supply curve?
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- 3. Suppose we are in a society where the social rate of time preference is 5% per year. The discount rate of utility is 3.5% per year, and the elasticity of marginal utility of consumption is 1.25. A. What is the assumed growth rate of future consumption under this scenario? B. Now assume the social rate of time preference changes to 10% while all else stays the same. What is the assumed new growth rate of future consumption? C. What does a SRTP of 5% mean compared to a SRTP of 10%? D. Why does the growth rate of future consumption change from one scenario to the other? ( If you Answer allow the above I will upvot definitely . ) Thank you5. 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.3. Suppose we are in a society where the social rate of time preference is 5% per year. The discount rate of utility is 3.5% per year, and the elasticity of marginal utility of consumption is 1.25. A. What is the assumed growth rate of future consumption under this scenario? B. Now assume the social rate of time preference changes to 10% while all else stays the same. What is the assumed new growth rate of future consumption? C. What does a SRTP of 5% mean compared to a SRTP of 10%? D. Why does the growth rate of future consumption change from one scenario to the other? Answer C & D
- Course: Microeconomics - Intertemporal Consumption Decisions Consider a person who consumes in the 2 periods (C1 and C2), but ONLY works and earns an income in the first period (C1). Assume that consumption in each period behaves as a normal good.a) What is the effect of a rise in income on welfare? And on consumption in both periods? GRAPHb) What is the effect of a rise in the interest rate (assume that r goes from 10% to 15%) that occurs before the consumption decisions on welfare? GRAPH and on consumption in both periods?) GRAPH3. A consumer maximises the following two-period utility function 1 V = max 1 ule,) + Fu(c) (1+p)? subject to the following 2-period budget constraint, C2 Ao + 1+r" (1+r)² Y2 1+r*(1+r)²' By choosing consumption at each period, c, and c2. r denotes the real interest rate, p is the time preference rate, Ao is initial wealth and y, and y2 represents incomes in period 1 and period 2 respectively. (a) Use the Lagrangian method to obtain the first order conditions for the utility maximisation problem and obtain the Euler equation. (b) Assume utility function has the form of u(c,) = 5 0.2 and r = 0.3. Obtain the equations/solutions for maximal c, and c2 by substituting the Euler equation back into the two-period budget constraint for the situations of either A, = -50 or Ao = 50. Explain the results. , Y1 = 200, y2 = 300, p = 0.63. Consider a simple Robinson Crusoe model where Crusoe gets utility from consump- tion c and leisure I as u(c. 1), where u is increasing, concave and differentiable in its arguments. Crusoe faces a production function of the form y = Af(n), where n = 1=1-1 and A is a productivity shock. (a) Depict Crusoe's optimum graphically. Discuss the income and substitution ef- fects on n of a change in A. Do these movements create comovement between consumption and output in this model? (b) Try to provide an exhaustive list of business cycle facts. (c) What business cycle facts does this model account for? 2
- Course: Introduction to Microeconomics Topic: Intertemporal Consumption DecisionsA consumer makes decision to consume in this year and next year. This year she has an income of M1 = $ 1.5 million and next year her income will be M2 = $ 2.75 million. Interest rate is 10%. Her intertemporal preferences are represented by function U(c1, c2) = c1*c2, whose intertemporal marginal rate of substitution is IMRS = c2/c1.a) Find and graph Budget Constraintb) Find and graph optimal consumption basket and indicate whether the consumer SAVES or BORROWS in the FIRST YEAR.c) Indicate whether following statement is true or false: "Any increase in interest rate will cause a decrease in consumer's welfare" Justify.d) If next year's income is maintained, how much would this year's income have to be for consumer to neither save nor borrow money at 10% interest rate?e) How much would interest rate have to be for consumer to consume exactly her initial endowment (M1 = $ 1.5 million and M2 = $ 2.75…Problem 2. Analyze the effects of the following events on the equilibrium values of the real wage, employment, output, the real interest rate, investment, saving and consumption. Your analysis should include appropriate graphs and a verbal explanation. (a) A natural disaster destroys a significant amount of the nation's capital stock. (b) A new innovation promises to increase the future marginal product of capital. (Assume that current desired consumption is unaffected by the increase in future income that would naturally follow from increased productivity.)2. What would be the impact of changing the determinant variables given in the first column (below) on investment? Factors affecting Investment Effect on Investment decrease in interest rate Increase in interest rate Increase in prices of capital goods There is no technology available in the country Demand for consumer goods decrease Government decided to increase corporation tax Increase in Subsidies
- a. Based on only the first-order condition with respect to labor computed in part a (Based on the given Lagrangian, compute the representative consumer's first-order conditions with respect to consumption and with respect to labor). Qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relation ship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes in / affect the relationship (shift it outward, shift it in inward, or impossible to determine). Briefly describe the economics of how you obtained your conclusions. (Note: In this question you are not to use the first-order condition with respect to consump tion nor any other conditions.) b. Now based on both of the two first-order conditions computed in part a, construct the consumption-leisure optimality condition. Clearly present the important steps and…Consider a forward-looking individual who aims at maximizing her lifetime utility from her lifetime resources. Assume the initial endowment of the individual isand her expected labour income is in the sequence Her utility function takes the form where is consumption in period and . Assume the real interest rate, is constant but not equal to the discount rate . Suppose that this individual lives for two periods, write down her intertemporal budget constraint and carefully interpret it. Explain why the lifetime budget constraint must be satisfied with a strict equality. From the intertemporal budget constraint, derive the permanent income hypothesis (PIH) and explain the drivers of consumption growth in this model.Which of the following is/are consistent with the neoclassical theory of distribution? (i) Everything else being constant, higher employment of a factor comes only at the expense of a lower return. (ii) The more abundant a factor is, the lower is its return. (iii) The more abundant a factor has become, the higher is the return of the factor which has not increased. a. (i), (ii), and (iii) are all correct. O b. O C. O d. Only (i) is correct. Only (iii) is correct. Only (ii) is correct.