MID-TERM EXAM #2: Intermediate Macro Winter 2014

Transcription

1 MID-TERM EXAM #2: Intermediate Macro Winter 2014 Name: Student Number: State clearly your assumptions when you derive a result. You must always show your thinking to get full credit. You have 1 hour and 20 minutes to answer all questions. Good luck. 1

2 Please leave this page blank for your grade. 2

3 Potential Output and Deficits Question 1 This paragraph is excerpted from a 2/28/2014 report by the Congressional Budget Office (CBO) This report examines a change in CBO s projections of potential output for the year 2017, comparing the projection it published in January 2007 with the one it released in February From the earlier projection to the more recent, CBO s projection for potential output in 2017 declined by 7.3 percent (see the figure below). [34 points] a) Please illustrate the concept of potential output. Answer: Potential GDP is real GDP after the economic fluctuations have been removed. 3

4 b) Please illustrate the concepts of headline deficit, structural deficit, primary deficit. Answer: Headline deficit is the actual deficit defined as: Headline deficit=g+tr+int-t where G, TR and INT denotes the government spending, transfers and interest payments respectively, and T is the tax received by the government. Assume G and TR have linear functional forms, i.e. TR=TR 0 -ay T=T 0 +by where Y denotes the actual output. The Headline deficit can be rewritten as Headline deficit=g+tr 0 +INT-T 0 -(a+b)y Structural deficit is the level of deficit when the output is the potential output, i.e. Structural deficit=g+tr 0 +INT-T 0 -(a+b)y* where Y* denotes the potential output. Primary deficit is derived after deducting the interest payments component from the total deficit, i.e. Primary deficit= G+TR-T =G+TR 0 -T 0 -(a+b)y c) Put yourself in the shoes of a financial analyst trying to assess the relevance to this CBO report for budgetary purposes. Is this good news for the US fiscal stance of the US government? Suppose the US government is currently in a fiscal position that is just right in terms of sustainability of the current fiscal position in the opinion of financial markets. What would be the implication of these news for market participants? Should the US government tighten its fiscal stance in terms of government spending and generosity of the automatic stabilizers? Explain. Answer: As is shown in the Equation (1), when the structural deficit Y* decreases, the structural deficit will increase. As result the US government s fiscal position will deteriorate. The government can improve its financial position (i.e. decreases its deficit by decreases its spending G and reduce the generosity of automatic stabilizer, a and b. 4

5 IS Curve Question 2 Which of the following situations move the IS curve? Describe the effect in the goods market first. [33 points] i. The Italian government decreases spending G (by reducing the level of capital investment in roads) r S(r)=Y0-C(r)-G r* r** S (r)=y0-c(r)-g I(r) IS IS S, I Y0 Y The saving curve is determined by S(r)=Y-G-C(r). When government expenditure decreases from G to G, the saving curve will shift outwards. To see this, given the same level of r, S(r) is larger. The equilibrium interest rate decreases from r* to r**. Consequentially, IS curve shifts in. Because given the same level of Y0, equilibrium interest rate decreases. ii. r The future TFP of the US is revised downwards (MPKf decreases). S(r)=Y0-C(r)-G r* r** I (r) I(r) IS IS S, I Y0 Y The firm s investment condition is determined by MPK=αA(K/N) α-1 =r. Given the same interest rate r, when A decreases, K will decreases. Therefore, when TFP goes down, firm will be discouraged to make investment. As a result, the investment curve shift inwards. The equilibrium interest rate decreases from r* to r**. Consequentially, IS curve shifts in. Because given the same level of Y0, equilibrium interest rate decreases. 5

6 iii. r The marginal propensity to save of the US economy decreases. S (r)=y0-c (r)-g r** r* S(r)=Y0-C(r)-G I(r) IS IS S, I Y0 Y The saving curve is determined by S(r)=Y-G-C(r). When the marginal propensity to save decreases, given the same income, households would like to consume more. Hence, the C(r) goes up and saving curve shift up. The equilibrium interest rate increases from r* to r**. Consequentially, IS curve shifts out. Because given the same level of Y0, equilibrium interest rate increases. iv. The U.S. Congress passed the Tax Reform Act (TRA) in It temporarily reduced personal income taxes. Assume people do not consider they have to repay whatever increases in government deficit this produces during their lifetime and do not care about future generations. r S (r)=y0-c (r)-g r** r* S(r)=Y0-C(r)-G I(r) IS IS S, I Y0 Y Savings in this economy are S(r)=Y0 - C(r) G (they are the sum of private saving Y). Note the private consumption is also determined by household s PVLR. When the tax rate decreases and will not bounce up in the future. From a consumer perspective, the PVLR increases. This drives up the private consumption, causing saving curve shift inward. The equilibrium interest rate increases from r* to r**. Consequentially, IS curve shifts out. Because given the same level of Y0, equilibrium interest rate increases 6

7 Consumption Question 3 Suppose Brunilde has labor income in period 1 of $50,000 and income in period 2 of 75,000. Wealth in period 1 is valued at $10,000 and she knows an inheritance will occur at period 2 in the amount of $30,000. Interest rates are 5%. Brunilde has logarithmic additive separable preferences with discount factor of 60% or U(c 1, c 2 ) = ln(c 1 ) +.6*ln(c 2 ) [33 points] i. Define the intertemporal budget constraint for Brunilde. Answer: The intertemporal budget constraint is c 1 c =y a y a From the question, we know that period 1 labor income y 1 and wealth a 1 are 50,000 and 10,000 respectively. Period 2 labor income y 2 and wealth a 2 are 75,000 and 30,000 respectively. Moreover, the interest rate is 5%. Substitute these numbers into the above equation and obtain c 1 c = ii. Find the point of no borrowing and no lending in terms of her consumption profile. Answer: The no borrowing and no lending consumption profile is c 1 =60000 ; c 2 = iii. Find Brunilde s optimum absent credit constraints. Answer: In absent of credit constraint, Brunilde solve the following optimization problem max c 1,c 2 U(c 1,c 2 ) ln(c 1 ) 0.6 ln(c 2 ) s.t. c 1 c =y a y a Transform this problem from a constrained optimization to an unconstrained one by substitution inside the utility function of c2 c which comes from the budget constraint. Now we take the first order conditions with respect to c 2 and set it to 0: 7

8 c1 c2 which is the Euler equation: c 2 0.6*1.05 c 1 Substituting it back to the intertemporal budget constraint, we have 1.6c or c 1 = Consequently c 2 = 0.6*1.05*100000=63000 iv. Find Brunilde s optimum under credit constraints. Answer: From part iii), we know that Brunilde would like to borrow against future and finance the first period s consumption. With the presence of the credit constraint, she is incapable of borrowing to reach her optimal consumption bundle. Suppose she has no access to credit at all, then her optimal consumption will be a corner solution to the optimization problem. In the first period, she will spend all her first period s income. In the second period, she will spend all that she is going to earn in that period. That is the optimum is c 1 =60000 ; c 2 =