Consumption and Investment

Transcription

1 Consumption and Investment PROBLEM SET 2 1 Consumption 1. What are the hypothesis of the Keynesian theory of consumption? 2. Consider an economy where the consumption function is the following: C = 0.82Y (1) where C is consumption and Y is the real income. Define and compute: (a) the marginal propensity to consume (MPC); (b) the average propensity to consume (APC) for several values of the national income: 2000, 4000, 6000, How does the APC change? (c) the elasticity of consumption to national income for the values of income in (b). What is the effect on consumption of an increase of 1% in the purchasing power of income? 3. Compute (a) the average and marginal propensity to save; (b) national savings and average propensity to save for the values of national income in question 2 (b). 4. Assume that the population of a country is composed of two different groups of agents (1 and 2). Group 1 earns two-thirds of the total national income (Y 1 = 2 3 Y ); group 2 earns the rest (Y 2 = 1 3Y ). Their consumption functions are the following: C 1 = 0.95Y (2) C 2 = 0.95Y (3) (a) Compute the aggregate consumption function of this economy. (b) Compute the average propensity to consume of the two groups of population when the national income is Given the Keynesian theory of consumption, which one of the two groups has the highest average revenue? 1

2 (c) The government decides to stimulate consumption by decreasing taxes by 100. Compute the increase in consumption. What is the most appropriate policy to stimulate aggregate consumption: increase in RMI or decrease in taxes on wealth (impôt de solidarité sur la fortune)? 2 The Model of Fisher 2.1 Exercise 1 Fisher assumes that consumers can save or borrow at a rate r. Assume now that they can save at a rate r s and borrow at a rate r b, with r b > r s. 1. What is the budget constraint of the consumer in the case of C 1 < Y 1? 2. And if C 1 > Y 1? 3. Represent graphically the two budget constraints. Identify the feasible combinations of current and future consumption. 4. Add the indifference curves to the graph. Show the three possible cases: (1) the consumer saves; (2) the consumer borrows; and, (3) he does not save nor borrow. 5. What determines the level of consumption in the first period in each of the three cases? 6. Explain why one euro gained at time t + T has a lower value at time t than an euro at time t. What is the discounted value of an amount of X euros received in T periods from today? 2.2 Exercise 2 Assume that a consumer lives for two periods and that his preferences are represented by the following utility function: U(C 1, C 2 ) = C a 1 C b 2 (4) with C 1 is the consumption in the first period and C 2 is the consumption in the second period. Determine the optimal consumption choices (C 1,C 2 ) as functions of income in the first and second period (exogenous Y 1,Y 2 ), and of the interest rate r. 3 Permanent Income Hypothesis The time series of the revenue R of a country si shown in the following table: 2

3 Year R Rt P Rt T C t AP C 1. Assume that the permanent income R P t is determined as the arithmetic average of current revenue and income of the three successive years. Compute the permanent revenue of year 1 to 7, and write it in the third row of the above table. 2. Compute the transitory income R T t (fourth row of the table). 3. The consumption of the households is a function of their permanent income as follows: C t = 0.80R P t (5) What is the marginal propensity to consume the permanent income? And the average propensity to consume? Compute the consumption of the households for year 1 to 7 (fifth row of the table). 4. Compute the average propensity to consume the current income, and write it on the sixth row of the table. Represent graphically the relationship (revenue, AP C). Is it consistent with the hypothesis of Keynes? 5. Explain the reasons of the existence of a consumption puzzle. Can the theory of permanent income provide a solution? Why? 4 Life Cycle Hypothesis Mister X starts working at the age of 25. He does not have any initial capital or savings, and gains a yearly income of 30,000 euros. He will retire at the age of 65. He will die at age 77. Assume that he does not earn any interest on his savings, and that he will not perceive any retirement transfers. 1. If he spends his income smoothly during his life, what will his yearly consumption be? Compute: (a) his average propensity to consume his current income during his working years; (b) his yearly savings; (c) the amount of savings (capital) that he has available at the time of retirement. 3

4 2. How does he modify his behavior if the retirement age changes to 70? Explain. 3. What if the retirement age is 65, but he will die at the age of 83? Explain. 4. Assume that Mister X inherits 360,000 euros at age 25, and that he prefers to consume everything before he dies. The age of retirement is 65. Compute the consumption and savings rates and compare them with those obtained in question 1. Explain. 5. The following table shows the average amount of wealth of households in 1992, by age. (Source: Economie et statistiques, June 1992) <25 years old > Does the behavior of households satisfy the hypothesis of the life cycle theory? 5 Questions 1. Referring to the different theories of aggregate consumption, discuss the impact of the variability of the current income on the choices of consumption. 2. How could inflation affect the behavior of households in terms of consumption choices? 3. Using the theory of intertemporal consumption of Fisher, explain why the impact of the interest rate on the consumption is ambiguous. You can make use of a graphical representation on the plan (C 1, C 2 ). 6 Investment 1. Define the notion of investment. What is the difference between the net and the gross investment? 2. What does represent the user cost of capital? 3. Based on the neoclassical theory of fixed investment of firms, under what conditions can the firms rent their capital to increase their stock? 4. A firm produces a quantity Y of goods using the technology represented by the following Cobb-Douglas production function: Y = AK α N 1 α (6) 4

5 with 0 < α < 1. K and N represent the stock of capital and the level of employment (stock of workers), respectively. The firm sells its goods at price P. Let W be the wage and Z the nominal cost to rent capital. (a) Write the profit function of the firm. (b) Determine the optimal demand for labor and for capital. Explain. (c) Assume that the firm employs the exogenous number of workers N. Derive the optimal demand for capital as a function of N, A, Z, P. (d) How does the marginal productivity of capital vary with the increase in the stock of capital? Show it algebraically. Represent the equilibrium of capital market in the plan (K, Z/P ). (e) Assume that the economy is affected by a negative oil shock which reduces the technology level A. How does it affect the investment decision of the firm? Show it in a graph. 5