2. Suppose that k(t) = koe0.09t and y = ka, where a = 1/3. a. (3 Points) What is the growth rate of y? b. (3 Points) Suppose that k(0) =

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)

Exercise 2 You are given the below variables: Price of the good itself Income Prices of related goods Tastes Expectations i. ii. iii. iv. V. State if a change in each of the variables results in a movement along the demand curve or a shift to the curve. Use several arguments to support your answer. (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.

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

(B) This question has to do with uncertainty regarding the rate of return to investment. The representative individual maximizes: EU = chy 1-y +BEL- -], y<1 where y> 0 is the coefficient of relative risk aversion. There is only one physical asset in the economy, namely capital. The individual has an initial wealth, W, consumes W-K in period 1, and saves (invest) the rest. The return from the investment is consumed in the second period. Thus C₂ = KZ, where Z is the stochastic return on capital. The log of Z is assumed to be normally distributed with mean and variance o² (obviously and o² refer to a different random variable here as compared to Question A(b)(ii) above). Thus the expectation of Z is e(+¹/2) (you are not required to know how to derive this). Note that if Z is lognormal, so are powers of Z. Hence the expectation of Z" is e(+¹²/2) (a) Calculate the optimal savings decision. (Note that Hall's Euler equation does not apply here. Why not?) How does an increase in ² affect saving? (b) Does your answer to part (a) say anything about the effects of an increase in uncertainty on savings? (See also question (c) below - in fact, you may wish to attempt (c) first.) (c) Holding constant the expectation of Z, how does saving respond to a change in o²? (d) How is your answer to (c) affected if y>1, and what is the economic rationale for this?

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)

5. In our personal lives, we sometimes need to react to changes in our economic environment. Thinking about your own budget, describe how a change in an economic variable (such as a change in income, employment, interest rates, or prices) from within the last year either has impacted or could impact your personal life and finances. If the trend continues over the next year or two, what predictions could you make about further impacts to your personal life and finances? [Write your response to question 5 here.]