Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible

Transcription

1 Midterm #1 ECON 322, Prof. DeBacker September 25, 2018 INSTRUCTIONS: Please read each question below carefully and respond to the questions in the space provided (use the back of pages if necessary). You must show your work. Please write clearly and indicate your answers You may use a calculator, but not the calculator on a phone or a graphing calculator. This midterm consists of the following two sections that total 100 points: Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible Good luck. Part 1: Short Answer (60 points possible, 3 points each) 1. What is macroeconomics? The study of the economy as a whole. Or something about studying economic aggregates. 2. What do we call variables that are determined within an economics model? Give one example of this type of variable from an economic model you are familiar with (doesn t have to be from this class). We call these endogenous variables. An example might be prices and quantities traded from a model of a market as seen in micro. Or, from the models we ve studied thus far; steady-state capital (Solow Growth Model), the real interest rate or investment (Market for Loanable Funds), the steady-state unemployment rate (the labor search model). 3. What did the circular flow model tell us about approaches to computing GDP? The circular flow model helps to illustrate the equivalence between the expenditure and income approaches to computing GDP. 4. Give an example of an economic variable that is a stock. Give an example of a variable that is measured as a flow. 1

2 A few stock variables that we ve talked about thus far: the capital stock, the money supply, the number of labor force participants. A few flow variables that we ve talked about: investment, GDP, consumption, inflation. Other examples are fine as well, as long as they are correct. 5. If people exit the workforce and there is no change in employment (i.e., the number employed stay the same), what happens to the unemployment rate? The unemployment rate will fall. To see this, note that we can find the number unemployed, U, as the difference between the number in the labor force, L, and the number employed, E. Thus, U = L E. Then, using the defintion of the unemployment rate, we can find: U L = L E L = 1 E L (0.1) Thus, if L falls and E is constant, then E L rises, which means taht U L falls. You might have also been able to sign the direction of the change by intuitively noting that if the number employed does not change and the number in the labor force falls, it must be that all those who dropped out of the labor force were unemployed, and thus the unemployment rate must go down. 2

3 6. Price indices based on a fixed basket of goods tend to overstate the rate of inflation. Understanding that this is the case, which measure would give higher real GDP in the year 1970 (measured in 2018 dollars) - one where nominal GDP in 1970 is deflated by the Consumer Price Index (CPI) or one where nominal GDP in 1970 is deflated using the GDP Deflator? Since we are going back in time, and there was positive inflation over this period, then putting 1970 GDP into 2018 dollars will mean that real GDP in 1970 will exceed nominal GDP in 1970 (since, due to inflation, a dollar in 2018 doesn t purchase as much as a dollar in 1970). The CPI is computed using a fixed basket, so would overstate inflation from these 48 years relative to the GDP Deflator. Thus, using the CPI to put 1970 GDP into 2018 dollars would yield a real GDP in 1970 that is higher than what one would find using the GDP Deflator. 7. What are the returns to scale in the production functions: Y = K 0.2 L 0.6? This is a Cobb-Douglas production function. We know that we can sum the exponents on the factor inputs to determine the returns to scale. Here we have = 0.8 < 1, which means that this production function exhibits decreasing returns to scale. 8. Draw a production function that exhibits a positive, but diminishing, marginal product of capital. You should have drawn a concave function with positive slope with Y and K on the axes. 3

4 9. Suppose that the marginal propensity to consume is 0.8 (for any amount of disposable income). By what amount does savings change if taxes go down by $50? The $50 tax cut increases disposable income by $50. Given an MPC of 0.8, consumption increases by 0.8 $50 = $40. The increase in savings is the remainder from the change in disposable income, $ Draw the model of the loanable funds market. Illustrate what happens to the equilibrium real interest rate if demand for investment increases. You should have a downward slowing investment function, with r on the vertical axis and I, S on the horizontal. The savings function would be vertical (or upward sloping). An increase in investment demand would shift the investment curve up and to the right. This would increase the equilibrium interest rate. It would not affect equilibrium investment if the savings curve is vertical, but would increase equilibrium investment if the savings curve were upward sloping. 11. Give one example of a policy or institution or market imperfection that keeps wages above their free, competitive market equilibrium. This could be minimum wage policies, labor unions, or asymmetric information that results in workers being paid efficiency wages. 4

5 12. Suppose the rate of job finding over a month is 0.1 and the rate of job separation is If there are currently 100 employed workers and 50 unemployed workers, how many employed and unemployed to we expect to have in one months time? We can find the number employed as E = 100 ( ) + (0.1 50) = = 103. The number unemployed can be found as U = 50 + ( ) (0.1 50) = = Using the assumptions from the previous question (a job finding rate of 0.1 and a separation rate of 0.02), what is the long-run (or steady-state) unemployment rate? The steady-state unemployment rate is a function of the finding and U separation rates: = 1 = 1 = 1 = 1 = or 16.7% unemployment L 1+ f s 0.02 rate. 14. Suppose that the aggregate production function is Y = F (K, L) = K 1 2 L 1 2. What is the per-worker production function? Because the production function is a Cobb-Douglas production function with constant returns to scale, we can find the per worker production function as: y = Y L = F (K L, L L ) = y = ( K L ) 1 2 ( L L ) 1 2 (0.2) = y = k 1 2 5

6 15. If the population growth rate falls from 5% to 1% (with no other changes), what happens to the steady-state capital per worker (not looking for a specific number, just a direction of change)? A decrease in the population growth rate would increase the steady state capital stock. On could find this using the condition that determines the steady-state capital stock: sf(k) = (δ + n)k or by seeing how the steady state changes in a graphical representation of the Solow Model as the slope of the curve for (δ + n)k becomes flatter. 16. Use a graph to illustrate the steady-state in the Solow Growth Model. The graph should show the investment function and depreciation function and note the steady-state capital stock at the intersection of these two curves. 17. What would be the likely effect of an elimination of tax preferences for retirement savings on the long run capital stock? Why? This policy change would likely have the effect of lowering the savings rate and thus the long-run capital stock. 6

7 18. If the economy currently has a capital stock that exceeds the golden rule capital stock, what might a benevolent government want to do? A benevolent government that cared about our long-run (and in this case also short-run) consumption would do something to decrease the savings rate. This could be a lowering of interest rates through monetary policy or tax changes related to savings. 19. List two instruments of monetary policy that the Federal Reserve can employ to directly change the monetary base. These could be any two from the following: open market operations, discount window lending, or the term auction facility. 20. Suppose that there is a crisis in student loan debt that causes a loss of value for bank assets (namely, the loans they made to students). This causes banks to hold more reserves. What happens to the money supply? The student loan crisis would likely have the effect of increasing the reserve deposit ratio of banks. This would lover the money multiplier and thereby lower the money supply. 7

8 Part 2: Analytical Problems (40 points possible) 21. Solow Growth Model (20 points). Consider the Solow Growth Model without population growth or technological change. Let f(k) = k 1 2 (recall that x 1 2 = x), δ = 0.1, s = 0.2, and k 1 = 4. (a) What is output per worker in period 1, y 1? y 1 = k 1 = 4 = 2 (b) What is the steady state capital stock, k? k can be solved for from the equation: sf(k) = δk: sf(k) = δk 0.2k 1 2 = 0.1k 2k 1 2 = k (0.3) Thus, k = 4. 2 = k = k (c) Suppose that the savings rate increases to 0.3. What is the new steady state capital stock? k can be solved for just as above, but with a new savings rate: sf(k) = δk 0.3k 1 2 = 0.1k 3k 1 2 = k (0.4) Thus, k = 9. (d) What is the golden rule capital stock? 3 = k = k kgold can be solved for from the equation: MP K = δ: Thus, k gold = 25. MP K = δ 1 2 k 1 2 = 0.1 k 1 2 = 0.2 k = k = k = 25 (0.5) 8

9 (e) What can you say about the savings rate that it will take to get to the golden rule capital stock? (Partial credit if you can say what it is relative to your answers to parts (b) and (c), full credit if you give the specific rate it takes to get there). It s clear that the savings rate has to be higher than even 0.3. To find the rate needed to reach kgold one can use the SS condition evaluated at kgold and solve for s: sf(k) = δk sf(k gold) = δk gold s( ) = s = 2.5 s = s = 0.5 (0.6) Thus, a savings rate of 0.5 is needed to reach k gold = 25. 9

10 22. The Market for Loanable Funds (20 points). Assume that real GDP, Y, can be decomposed into aggregate consumption, C, aggregate investment, I, and government spending, G, in the following way: Y = C + I + G. Furthermore, assume that real GDP is fixed because capital and labor are fixed: Ȳ = F ( K, L) = K α L 1 α. Let α = 1 2 (and note that x 1 2 = x). Assume that government spending, Ḡ, is fixed and that net taxes, T, are fixed. Also, assume that consumption is a positive function of disposable income in the following way; C = C( Ȳ T ) = 0.9(Ȳ T ), and is therefore fixed. Lastly, assume that investment, I(r), is a negative function of the real interest rate r, such that when r goes up, I goes down, and vice versa. Specifically, let I(r) = r. Let the exogenous variables take on the following values: K = 400, L = 900, Ḡ = 100, T = 200. (a) Solve for the equilibrium real interest rate and investment in the market for loanable funds. First, determine national income as Y = F (K, L) = = = 600. We can then find national savings as: S = Y C G S = Y 0.9(Y T ) G S = ( ) 100 S = 140 (0.7) With the equation for national savings, we use the equilibrium condition from the market for loanable funds: S = I(r) to solve the the equilibrium interest rate and investment: I = S r = r = 60 r = 6 (0.8) Thus, the equilibrium real interest rate is 6 and the equilibrium amount of investment is 140. (b) Suppose that Congress passes, and the President signs, a large tax cut, which lowers T to 100. What happens to the equilibrium real interest rate? Investment? Save steps as above... now S = ( ) 100 = 50. With the equation for national savings, we use the equilibrium condition from the market for loanable funds: S = I(r) to solve the the equilibrium interest rate and investment: I = S r = r = 150 r = 15 (0.9)

11 Thus, the equilibrium real interest rate is 15 and the equilibrium amount of investment is 50. (c) How would your answer to part (b) change if the marginal propensity to consume were lower than 0.9? (Looking for a qualitative answer only) If the MPC were lower, households would save more of the tax cut. This would result in less of a decline in national savings and investment and a smaller increase in interest rates than with an MPC of 0.9. (d) Think about the very long run effects of the change in investment/savings you found in part (b). What might be the consequences on economic growth of the tax cut in the context of the Solow Growth Model? The tax cuts lower national savings. A lower savings rate will slow economic growth and lower the steady-state capital stock. 11