Numerade

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Shu Naito

Numerade educator

BONUS. Determine the stability properties of the steady-states for each case and each and every steady-state point. PLEASE USE THE BACK SIDE OF THIS SHEET FOR YOUR ANSWER TO QUESTION 3.]

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Shu Naito

Numerade educator

Student ID 2200794018 QUESTION 1 (20 points) A model of consumption (c) and wealth (w) is defined by the following equations: c[t] = ? w[t] w[t+1] + c[t] = ? w[t] Here, we have ? > ? > 0. Draw diagrams that describe the movement of the system in time for any possible starting point. w[t+1] + c[t] = ? w[t] w[t+1] + ? w[t] = ? w[t] w[(1+?] + ?) = ? w[t] 1 + ? - ? = -? 1 + ? + ? = ? (10 points)

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Shu Naito

Numerade educator

QUESTION 3 (20 points) Imagine a large number of firms in a continuous-time universe. You can normalize the total mass to unity so that f ? [0,1] indexes these firms. Let Yf,t denote firm f's investment at time t. We have Yf,t = G(Xt) where G is some non-decreasing function of Xt, and Xt is the expected (or average) investment level. Notice that G has the same functional form for all firms; it does not depend on f. Find all of the steady-state equilibria for the following (alternative) formulations of G: i. G(X) = ? X + ? (0 < ? < 1, ? > 0) ii. G(X) = X iii. G(X) = X² BONUS. Determine the stability properties of the steady-states for each case and each and every steady-state point.

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There are three fundamental causes of long-run economic growth. Fill in the following schema with these causes and the relationships among them (Note: Rectangles are for the causes, and dashed ellipses are for arrows.)

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Suppose that GDP per worker \( (\mathbf{y}) \) is determined by productivity \( (\mathbf{A}) \), physical capital per worker \( (\mathbf{k}) \) and human capital per worker \( (\mathbf{h}) \) as in \( \mathbf{y}=\mathrm{A} \mathbf{k}^{1 / 2} \mathbf{h}^{1 / 2} \) - Suppose that \( \mathbf{h} \) is constant (exhibiting no growth). Write down the mathematical relationship among the growth rates of \( \mathbf{y}, \mathbf{A} \) and \( \mathbf{k} \). - Let the growth rate of \( \mathbf{y} \) is \( 3 \% \) per annum and of \( \mathbf{k} \) is \( 1 \% \) per annum. What is the growth rate of \( \mathbf{A} \) equal to? - Would you advise the government to support R\&D investments of the firms instead of supporting education and health investments of households? Why, or why not?

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Give brief definitions or explanations of the following terms or concepts: - Life expectancy - Total fertility rate - Dependency ratio

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The following figure shows the two-way relationship between health and income per capita. Suppose that there was a government reformation program in the health system, resulting in increased access to health services at all income levels across the country. - Provide a graphical analysis of the effects of this reformation program on health (h) and income per capita (y). - Discuss your results in detail with a focus on whether this is a satisfactory model of human capital.

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Breanna Ollech

Numerade educator

Imagine the one-country model of technological change. There are two things produced; knowledge A and consumption good Y. The production functions are given as Y = A LY ?A = 3 LA A LY and LA denote the numbers of workers allocated to Y production and A production, respectively. In this economy, there are 10 million workers in total: LY + LA = 10 (Hint: The growth rate of variable x is defined as in x = ?x / x.) - Suppose that 2 workers are assigned to the knowledge production. What is GDP per worker (y) equal to? - What is the growth rate ? of knowledge equal to? - What is the growth rate ? of GDP per worker equal to? - Suppose that there was an improvement in knowledge production such that ?A = 5 LA A. What should this economy do to keep the growth rates unchanged?

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