ECN101: Intermediate Macroeconomic Theory TA Section

Transcription

1 ECN101: Intermediate Macroeconomic Theory TA Section Department of Economics, UC Davis December 1, 2014 Slides revised: December 1, 2014

2 Outline 1 Final Exam Information 2 Problem Set #4 Review Q.2 - How much is a college education worth? Q.5 - Quantity Theory of Money Q.6 - Asset Pricing Theory: A Coupon Bond Q.7 - Asset Pricing Theory: Term Structure 3 Problem Set #5 Preview Q.1 - Calculations with the IS Curve Q.2 - Analyzing Macroeconomic Events with the IS Cureve(II) Q.3 - Imports and the Multiplier 4 Past Exam Questions LQ1: IS Curve

3 Final Exam Information Two weeks later from tomorrow! Final Exam (50%) : December 16, Tuesday, 10:30 a.m. - 12:30 p.m. 10 MC + 2 SQ + 2 LQ? make-up office hour next Thursday? Monday in the final week? Review sessions with past exam on December 12 (Fri.) 1:10-3:00 p.m. at 194 Young by TA Seungduck Lee 3:10-5:00 p.m. at 194 Young by TA Jae Wook Jung on December 11 (Thursday) 3:10-5:00 p.m. place TBD 5:10-7:00 p.m. place TBD 7:10-9:00 p.m. place TBD

4 Q.2 - How much is a college education worth? Q.2 - How much is a college education worth?, Ch.7 Exercise 8 Suppose that college education raises a person s wage by $30,000 per year, from $40,000 to $70,000. Assume the interest rate is 3% and there is no growth in wages. Suppose you are a high school senior and deciding whether or not to go to college. Find the present discounted value of earnings in the following cases. Also, assume that the work time is still 45 years, adding up to a 49-year non-college work career. a) What is the PDV of your labor income if you do not go to college and start working immediately? A: ( R 1 ( 1 1+R ) 49 ) = $

5 Q.2 - How much is a college education worth? Q.2 - How much is a college education worth?, Ch.7 Exercise 8 b) As an alternative, you could pay $20,000 per year in college tuition, attend for 4 years, and then earn $70,000 per year after you graduate. What is the present discounted value of your net earnings (adjusting for tuition) under this plan? (Compute this value from the point of view of a high school senior.) c) Discuss the economic value of a college education.

6 Q.2 - How much is a college education worth? Q.2 - How much is a college education worth?, Ch.7 Exercise 8 A: Total career is 45 for a college graduate. Again, assume that now is the point of high school graduation and paying the first tuition for college. The first income will be paid in the fifth year, the first year after graduation from college. Thus, (pdv) of total income is ( ( 1 ) 4 1 (pdv) = R 1 ) R ( 1 1+R ) = $ Need to substract (pdv) of total tuition paid for four years from this

7 Q.2 - How much is a college education worth? Q.2 - How much is a college education worth?, Ch.7 Exercise 8 Time of paying the first tuition is assumed now. So, no discouting needs for the initial tuition value. (pdv) of total tuition for 4 years is ( ) (pdv) = Thus, (pdv) of total net income is ( 1 1+R 1 1+R ) = $76572 (pdv) = $ $76572 = $

8 Q.2 - How much is a college education worth? Q.2 - How much is a college education worth?, Ch.7 Exercise 8 d) What if you pursue the plan described in (b), but you also expect to be unemployed for 2 years after finishing college (knock on wood). During these years assume that you do not have access to any unemployment insurance. What is the PDV of your net earnings under this plan? e) A: Now, the first income will be paid in the seventh year, the third year after graduation from collge. Thus, (pdv) of net earning is f) ( ( 1 ) 6 1 (pdv) = R 1 ) R ( 1 1+R ) = $

9 Q.5 - Quantity Theory of Money Q.5 - Quantity Theory of Money Suppose velocity is constant, the growth rate of real GDP is 3 percent per year, and the growth rate of money is 5 per cent per year. Calculate the long-run rate of inflation in the following cases: a) What is the rate of inflation in this baseline case? From MV = PY, g M + g V = g P + g Y. the inflation rate π g P. Use given numbers, g Y = 3% and g M = 5%. What is g V? b) Suppose the growth rate of money rises to 10 percent per year. c) Suppose the growth rate of money rises to 100 percent per year. d) Back to the baseline case, suppose real GDP growth rises to 5 percent per year. e) Back to the baseline case, assume that velocity of money rises at 1 percent per year. What happens to inflation in this case? Why might velocity change in this fashion? Make your own story about changing the velocity of money.

10 Q.6 - Asset Pricing Theory: A Coupon Bond Q.6 - Asset Pricing Theory: A Coupon Bond Consider a coupon bond with maturity date n = 2 and face value F = 40. If you know that the supply of this bond is given by and the demand by S : P = 2Q D : P = 100 2Q a) Calculate the interest rate of this bond if the coupon payments are given by c = 10. What is the price of the bond, P? P = 50 and Q = 25. Which of asset pricing formula do you need? Quadratic formula: For ax 2 + bx + c = 0, x = b ± b 2 4ac 2a

11 Q.6 - Asset Pricing Theory: A Coupon Bond Q.6 - Asset Pricing Theory: A Coupon Bond b) Now suppose you do not know the value of c. Very often in reality, the amount paid by each coupon is a fraction x of the face value of the bond, in other words, c = xf, where x [0, 1]. Given this, if you know that the equilibrium interest rate of the bond in this question is i = 0.1, then what is the so-called coupon rate x of this bond? c) How do you expect the equilibrium interest rate of this bond to change if the expected returns of high-tech firms stocks increase? (no calculations needed here)

12 Q.7 - Asset Pricing Theory: Term Structure Q.7 - Asset Pricing Theory: Term Structure Suppose you live in period t (present) in a world where there are only 3 types of assets: 1-year T-bills, 2-year T-bills, and 6-year T-bills. For simplicity assume that people care about the next 6 years of their lives, and they cannot sell short. This means that if they buy a bond of maturity n, they have to keep it until period t + n (the maturity date). People can buy 1-year bonds in every single period (t, t + 1,, t + 5). Also, they can buy 2-year bonds in period t (that mature in t + 2), in period t + 2 (that mature in t + 4), and in t + 4 (that mature in t + 6). Throughout this problem please use notation similar to Chapter 6 of your textbook (for example i2,t+2 e will be the expected interest rate of the 2-year bond that agents can buy in period t + 2).

13 Q.7 - Asset Pricing Theory: Term Structure Q.7 - Asset Pricing Theory: Term Structure a) Suppose these assets are perfect substitutes. What will happen to the interest rate of 2-year (i 2,t ) and 6-year (i 6,t ) T-bills bought in period t if the supply of 1-year T-bills shifts out? Supply of 1-year bond = P 1 i 1 By the expectation theory, i 2 and i 6 move together, because increasing supply of 1-year bond affects (decreases) the demand for 2-year bond and 6-year bond (Every bond is a perfect substitute for others.) So P 2 and P 6 decrease and the interest rates go up. b) Now consider the other extreme: these assets are not substitutes at all. Is the interest rate (in period t) of 2-year bonds higher or lower than the one of 6-year bonds? How will an outward shift of the supply of 1-year T-bills in period t affect the interest rate of 6-year bonds? Normally the interest rate of 2-year bonds are higher than the one of 6-year bonds because of liquidity premium on 6-year bonds. Since 6-year bonds are not substitutes at all for 1-year T-bills, the interest rate of bonds moves independently.

14 Q.7 - Asset Pricing Theory: Term Structure Q.7 - Asset Pricing Theory: Term Structure Now consider an environment which is a combination of the ones described above. In particular, the assets are substitutes, but not perfect. People prefer short term bonds (because they are more liquid), but they would be willing to buy some bigger maturity bonds for the right return, a.k.a. premium. Let the premium of the asset of maturity n which is bought in period t be given by l n,t = 0.01(n 1) c) Suppose that the interest rate of 1-year bonds is expected to stay constant at 10 per cent over the next 5 years. Then calculate the interest rate (in period t) of 2-year and 6-year bills. Use your calculations to plot the yield curve of different maturity T-bills as of period t. i 2,t = i 1,t + i e 1,t l 2,t = = 0.11 i 6,t = i 1,t + i e 1,t+1 + ie 1,t ie 1,t l 6,t = = 0.15

15 Q.1 - Calculations with the IS Curve Q.1 - Calculations with the IS Curve, Ch.11 Exercise 1 Suppose the parameters of the IS curve are ā = 0, b = 3/4, r = 0.02, and the real interest rate is initially R = Explain what happens to short run output in each of the following scenarios (consider each one separately). a) R rises to 4 percent. b) R falls to 1 percent. c) ā c increases by 1 percentage point. d) ā g decreases by 2 percentage points. e) ā im decreases by 2 percentage points. : IS curve equation (11.12) is Ỹt = ā b(r t r). where ā ā c + ā i + ā g + ā ex ā im 1.

16 Q.2 - Analyzing Macroeconomic Events with the IS Cureve(II) Q.2 - Analyzing Macroeconomic Events with the IS Cureve(II), Ch.11 Exercise 3 For each of the following changes in the macro-economy, show how to think about them using the IS curve, and explain how GDP is affected in the shortrun. a) The government offers a temporary tax credit: for each dollar of investment that firms undertake, they receive a credit that reduces the taxes they pay on corporate income. : This is an increase in ā i : This is an intercept shift, not a slope shift! Why?

17 Q.2 - Analyzing Macroeconomic Events with the IS Cureve(II) Q.2 - Analyzing Macroeconomic Events with the IS Cureve(II), Ch.11 Exercise 3 b) A booming economy in Asia this year leads to an unexpected increase of the demand of Asian consumers for US goods. c) US consumers suddenly appreciate French products and sharply increase their imports from that country. d) A housing bubble bursts, so that housing prices fall by 20 percent and new home sales drop sharply.

18 Q.3 - Imports and the Multiplier Q.3 - Imports and the Multiplier, Ch.11 Exercise 8 Suppose that the amount of goods that the US imports depends not only on potential output (as in our baseline model), but also on the current state of the economy. In other words, when the economy is booming, imports go up. To incorporate this channel into the model assume that IM t = ā im + nỹt Ȳ t The rest of the model remains unchanged. a) Derive the new IS curve under this specification. : (11.9) will be changed to Y t Ȳ t = ā c + ā i b(r t r) + ā g + ā ex ā im nỹt b) How does the parameter n show up in the new IS curve? What is the economic explanation for that?

19 LQ1: IS Curve LQ1: IS Curve Consider the short run model of Chapters 11 and 12. The national income identity is given by Y t = C t + I t + G t + EX t IM t (1) where Y t is real actual output, C t is consumption, I t is investment, G t is government spending, EX t is exports, and IM t is imports (all in period t). Assume that the demand variables are given by: C t/ȳt = āc + xỹt (2) G t/ȳt = āg (3) EX t/ȳt = āex (4) IM t/ȳt = ā im (5) I t/ȳt = ā i b(r t r), (6) where ā c, ā g, ā ex, ā im, ā i, x, and b are given positive parameters. Moreover, Ȳt represents potential output, Ỹt is short-run output, Rt is the real interest rate, and r is the marginal product of capital or just the long run interest rate.

20 LQ1: IS Curve LQ1: IS Curve a) Combine equations (2)-(6) with (1) to obtain the IS curve. This curve should have short run output on the left-hand side and the real interest rate on the right-hand side. b) What is the meaning of equation (2)? Do we have any empirical evidence justifying the existence of the term xỹt in the consumption equation? c) Assume that ā c = 0.5, ā g = 0.3, ā ex = 0.15, ā im = 0.2, ā i = 0.25, b = 0.8, r = 0.1, and x = 0.1. Draw a graph with the IS and the MP curve in the long run. For the MP curve assume that the FED just sets R t equal to the long run interest rate.

21 LQ1: IS Curve LQ1: IS Curve d) Suppose that, because of the bursting of a bubble in real estate, the consumer and investor confidence declines. As a result, the terms ā c and ā i temporarily change to ā c = 0.47 and ā i = Draw the new IS-MP diagram. What is the new equilibrium R and Ỹ? (assuming that there is no policy intervention) e) If you were the chairman of the FED, and your objective was to bring short-run output back to normal (back to zero) fast, how would you change the real interest rate?