3. Consumption Problem. Suppose period utility is of the constant relative risk
aversion type:
u(c) --0-1,0>0.
Consumer's objective is to maximise expected lifetime utility:
=
U = E[Σ_Bu(c)], βε(0,1),
Eolt
t-0
with 3 = p > 0. Assume the real interest rate, r, is constant but not necessary
equal to the time preference, p. Eo is the expectation conditional on information at
time 0. The budget constraint is:
c+at+1 = yr + (1+r)at,
where do is given, yt is a stochastic random variable and at time t the consumer
knows the realisation of y, but does not know its future values.
a. What is the Euler equation relating the marginal utility of ce to expectations
concerning the marginal utility of C++1? Explain.
b. Suppose that the (natural) logarithm of income is normally distributed with
zero mean, and that as a consequence the logarithm of ce+1 is also normally
distributed, with mean E₂(lnc+1). Let o² denote the variance of the log of con-
sumption conditional on information available at time t. Rewrite the expression
in part (a) in terms of In(c₂), E₂(ln(+1), ² and the parameters r, p, and 0.
(Hint: If a variable z is distributed normally with mean and variance V, then
E(e²) = c+V).
c. Show that if rand o are constant over time, the result in part (b) implies that the
log of consumption follows a random walk with drift: In(+1) = a+ln(c₂)+u+1,
where u is a white noise.
d. How do changes in each of r and o² affect expected consumption growth,
E₂(ln(+1)-In())? Interpret the effect of o² on expected consumption growth
in light of the discussion on precautionary savings in Romer.
2
Fig: 1
Most Viewed Questions Of Advanced Macroeconomics
2. Solow model with Human capital. Consider the following Solow growth model with human capital a la Mankiw, Romer and Weil (1992). "A Contribution to the Empirics of Economic Growth," Quar- terly Journal of Economics 107, 407-437. They treated physical and human capital symmetrically Production function: Y(t) = (A(t)L(t))¹-a-³H(t)³K(t)ª, a, 3 € (0, 1), a + ß < 1. Capital accumulation: K(t) = 8kY(t) — 5K(t), 6, 8k € (0,1). Technical progress: A(t) = est A(0). Population growth: L(t) = entL(0). Human capital accumulation: Ĥ(t) = 8HY(t) - 5H(t), 6, 8H € (0,1). Society invests SH and SK percent of its total income Y in human capital and physical capital, respectively. a. What is the long run (Balanced Growth Path) growth rate of output per capita. Does it depend on sh? 1 b. Write down the stationary system and find out the steady-state level of output, physical and human capital per unit of efficiency labor. Show the dynamics of this system. c. This model augmented with human capital can be tested empirically with cross- country data if we assume that all countries are in the steady-state. Derive a log-linear regression equation for output per worker in the long run. d. Discuss the empirical findings of Mankiw, Romer and Weil (1992). Also, what are the main concerns with their empirical strategy?
Use the outreg2-command to generate an Excel table called "2a" containing all results from the loops below. Do not report the constants in the output table. /* Code: */ local Controls "i.country_survey left right male young children_dummy rich university_degree immigrant moved_up" eststo clear foreach var in budget_health budget_defense { eststo: xi: reg `var' q1_to_q1 `Controls' } foreach var in budget_health budget_defense { eststo: xi: reg `var' q1_to_q5 `Controls' }
Exercise 3 You are given the below variables: Price of the good itself Input prices ii. iii. Technology Expectations iv. V. Number of sellers 2 NICA UNIVERSIT State if a change in each of the variables results in a movement along the supply curve or a shift to the curve. Use several arguments to support your answer. (25 marks)
Exercise 4 Analyze using examples The Circular-Flow Diagram. FIRMS Revenue (= GDP) Goods and services sold Factors of production Wages, rent, and profit (= GDP) MARKETS FOR GOODS AND SERVICES MARKETS FOR FACTORS OF PRODUCTION Spending (= GDP) Goods and services bought HOUSEHOLDS Labor, land, and capital Income (= GDP) Figure 1: Mankiw, N.G., 2017. Principles of macroeconomics. Boston: Cengage Learning. = Flow of inputs and outputs = Flow of dollars (25 marks)
1. Solow model. Consider the standard Solow growth model with technological progress (g) and pop- ulation growth (n), where g and n are positive and exogenous. Assume that the economy is initially on the balance growth path. Suddenly there is a one-time unex- pected and permanent downward jump in the number of workers due to a government repatriation program of illegal immigrants. Explain both the immediate and transitional effect of this jump on capital per ef- fective worker and output per effective worker. Draw the time path of output per capita and compare it to the case without the repatriation program.
Exercise 1 You are given the below information: Price of Ice-Cream Cone $0 1 2 3 st 4 5 6 Catherine 12 10 8 6 4 2 0 Nicholas 7 6 5 3 2 1 Draw the market demand curve and calculate the market demand for each price. (25 marks)
1. In the first four weeks of this course, you have learned about economic concepts such as supply and demand, scarcity, tradeoff decisions, international trade, opportunity cost, and compound growth. Think about the economic concepts you encountered in the readings for the first three weeks, or those you know about from previously learning or research. These could include concepts such as supply and demand, scarcity, tradeoff decisions, inflation, and opportunity costs. Choose at least one economic concept and describe how it is relevant to the scenario and your two budgets. Write your response to question 1 here.]
5. (9 Points) Consider a Solow economy that begins in steady state. Then a strong earthquake destroys half of the capital stock. Use a Solow diagram to explain how the economy evolves over time. Draw one graph showing the time path of the log level of output per worker (y) and another showing the time path of output per worker's growth rate ().
