Here are 3 short question of macro econ

Economics

UCI

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PART B: Short Questions Short Question 1: (20 points) Answer the following parts: a. Assume a standard Cobb-Douglas production function that takes the form: Yt = AKtα Lt1−α . We will use this production for two countries, US and Brazil. In the data, capital per person in Brazil is 0.202 times that of the US. Let capital share be 1/3. Calculate the output per person in Brazil relative to the US if Brazil and US had same value of A? (5 points) b. Now, lets say that the observed per-capita GDP of Brazil is 0.252 times that of the US. What is the implied value of A for Brazil (relative to US) if you wanted to fit the production function model correctly (5 points) c) Give two examples that could explain differences in A between US and Brazil? (5 points) 5 d) In Chapter 2, we study the use of various ways to construct real GDP. Explain briefly why do we prefer to use chain-weighted index? (5 points) Short Question 2: (20 points) Consider the following aggregate production function. Y = AK α Lβ . A firm hires labor at wage rate w, and rents capital at rental rate r. (a) Write down the first order conditions for firm’s demand for labor and firm’s demand for capital (4 points) (b) What must be true about the parameters α, and β if this production function exhibits constant returns to scale? (2 points) 6 (c) A pandemic decimates labor force in the economy. What happens to the wage rate following a pandemic? How do you expect the wage rate to evolve over time as the population grows back? (6 points) Hint: your answer must have a plot of wage rate over time 1 2 (d) Assume Yt = At Kt3 Lt3 . TFP growth of a country is 2%, and capital growth of a country is 3%. If the labor growth rate was -2% in that year, what would have been the growth rate of real wage and the growth rate of rental rate (8 points) 7 Short Question 3: (30 points) Consider the standard Solow model. The expression for output and the dynamics of capital are given by the following expression: Y = AK α L1−α ∆K = sY − δK where δ > 0 (constant) is the depreciation rate of capital, s is savings rate of a country (also constant). Assume labor is fixed at L̄. (a) Using a Solow diagram, show the steady state level of capital. (label the x-axis and functions that you plot and mark the steady state level of capital) (8 points) 8 (b) Find an algebraic expression for the steady state capital per worker. Show your steps. (6 points) (c) Suppose a country is in steady state. An unfortunate event kills a significant portion of the labor force. Assume this is a permanent reduction in labor force. Using the Solow-diagram, explain what happens to the growth rate of output in the economy in the short-run? What happens to the level of output in the long-run? (10 points) (Hint: your answer should include an explanation with the Solow diagram plot) 9 (d) What if the one-time shock had destroyed capital stock instead of a reduction in labor force? ( 6 points) 10 PART B: Short Questions Short Question 1: (20 points) Answer the following parts: a. Assume a standard Cobb-Douglas production function that takes the form: Yt = AKtα Lt1−α . We will use this production for two countries, US and Brazil. In the data, capital per person in Brazil is 0.202 times that of the US. Let capital share be 1/3. Calculate the output per person in Brazil relative to the US if Brazil and US had same value of A? (5 points) b. Now, lets say that the observed per-capita GDP of Brazil is 0.252 times that of the US. What is the implied value of A for Brazil (relative to US) if you wanted to fit the production function model correctly (5 points) c) Give two examples that could explain differences in A between US and Brazil? (5 points) 5 d) In Chapter 2, we study the use of various ways to construct real GDP. Explain briefly why do we prefer to use chain-weighted index? (5 points) Short Question 2: (20 points) Consider the following aggregate production function. Y = AK α Lβ . A firm hires labor at wage rate w, and rents capital at rental rate r. (a) Write down the first order conditions for firm’s demand for labor and firm’s demand for capital (4 points) (b) What must be true about the parameters α, and β if this production function exhibits constant returns to scale? (2 points) 6 (c) A pandemic decimates labor force in the economy. What happens to the wage rate following a pandemic? How do you expect the wage rate to evolve over time as the population grows back? (6 points) Hint: your answer must have a plot of wage rate over time 1 2 (d) Assume Yt = At Kt3 Lt3 . TFP growth of a country is 2%, and capital growth of a country is 3%. If the labor growth rate was -2% in that year, what would have been the growth rate of real wage and the growth rate of rental rate (8 points) 7 Short Question 3: (30 points) Consider the standard Solow model. The expression for output and the dynamics of capital are given by the following expression: Y = AK α L1−α ∆K = sY − δK where δ > 0 (constant) is the depreciation rate of capital, s is savings rate of a country (also constant). Assume labor is fixed at L̄. (a) Using a Solow diagram, show the steady state level of capital. (label the x-axis and functions that you plot and mark the steady state level of capital) (8 points) 8 (b) Find an algebraic expression for the steady state capital per worker. Show your steps. (6 points) (c) Suppose a country is in steady state. An unfortunate event kills a significant portion of the labor force. Assume this is a permanent reduction in labor force. Using the Solow-diagram, explain what happens to the growth rate of output in the economy in the short-run? What happens to the level of output in the long-run? (10 points) (Hint: your answer should include an explanation with the Solow diagram plot) 9 (d) What if the one-time shock had destroyed capital stock instead of a reduction in labor force? ( 6 points) 10 ...
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