Copenhagen Business School, Department of Economics, Birthe Larsen Question A Retake Exam in Macroeconomics, IB and IBP Answers 4hoursclosedbookexam 14th of August 2009 All questions, A,B,C and D are weighted equally Regard the following model for a closed economy: 1. E = C + I + G, 2. C = c 0 +0.5(Y T ), 3. I = 50 100r 4. Y = E. 5. M d /P =0.75Y 100r 6. M d /P = M/P Where C is consumption, Y is output and income, I is investment, G is government spending, T is the tax, E is planned expenditure, M is money supply, r is the real interest rate, P is the price level and M d is money demand. The variables E,C,I,Y,M d and r are endogenous, T,P,M and G are exogenous. Let T = 100, G = 100, M= 75,P =1,c 0 = 100. 1) Derive and draw the IS curve. 1) Derive and draw the IS curve. We insert equation 1,2 and 3 into equation 4toobtain: Y = 100 + 0.5(Y 100) + 50 100r + 100, 0.5Y = 200 100r, r = 2 0.005Y. See Figure 1. 2) Derive and draw the LM curve. Insert equation 6 into equation 5 to obtain: r =0.0075 Y 0.75 The LM curve is drawn into Figure 1. 3) Find the equilibrium level of output and indicate the equilibrium in the IS-LM diagram. 1
Insert the LM curve into the IS curve to obtain: 0.5Y = 200 100 (0.0075Y 0.75), Y = 1 275 = 220 1.25 Then insert the equilibrium output level into the IS curve (or the LM curve) to obtain: r =0.0075 220 0.75 = 0.9 The equilibrium, (Y,r) = (220; 0.9) is indicated in Figure 1. 4) Suppose now that the economy faces a recession corresponding to reduction of c 0 to 75. Which curve is shifting? Derive and draw the new curve and find the new equilibrium. The IS curve shifts downwards to Y = 75 + 0.5(Y 100) + 50 100r + 100, 0.5Y = 175 100r, The new equilibrum is then r = 1.75 0.005Y. 0.5 Y = 175 100 (0.0075 Y 0.75), Y = 1 250 = 200 1.25 r = 0.0075 200 0.75 = 0.75 The new IS curve and the new equilibrium, (Y,r) = (200; 0.75) is indicated in Figure 2. 5) Explain verbally how the reduction in autonomous consumption a ects output. A reduction in c 0 reduces consumption for given interest rate (eq. 2) and thereby planned expenditure (eq. 1) which reduces output (eq. 4). When output falls, disposable income falls and thereby consumption (eq. 2). The decrease is larger the larger the marginal propensity to consume is. In this case it is c 1 =0.5. Reducedconsumptionreducesplannedexpenditureandthereby output again, which again reduces disposable income and consumption. However, lower output also reduces money demand (eq. 5) and for given money supply, the result is a lower interest rate. The reduced interest rate implies that investment increases (eq. 3) which again increases planned expenditure (eq. 1) and output, modifying the equilibrium reduction of output. Question B Consider the same economy as in question A. 2
1. Suppose the economy chooses to combat the recession by increasing government spending. Illustrate this by increasing government spending to G = 125. WhathappenstoOutput?Outputincreasesto: 0.5 Y = 175 100 (0.0075 Y 0.75) + G 0.5 Y = 175 100 (0.0075 Y 0.75) + 25 Y = 1 275 = 220, 1.25 i.e gets back to the original equilibrium. Show the implied IS curve in the IS-LM diagram and indicate the equilibrium: As the first graph. 2. What happens to the government budget deficit? The government budget deficit, G T increase from G T = 100 100 = 0 to G T = 125 100 = 25. 3. Is a government budget deficit a problem. The problem is that it will increase the government debt. However if the budget deficit is reduced again, when the economy is booming, it is not necessarily a problem. 4. Suppose now that the government instead chooses to let the economy be less sensitive to shocks by introducing automatic stabilizes. Define and suggest how an automatic stabilizer can be introduced in the model. Definition: policies that stimulate or depress the economy when necessary without any deliberate policy change. An automatic stabilizer could be an income tax or unemployment insurance. Income tax could be introduced in equation 2. We would then need to include a new equation, 7, determing the tax rate, which then would be endogenous, like: 7. T = t 0 +t 1 Y.Alternativelyunemploymentinsurancecouldbeincluded. However, we have not talked about including this variable during lectures or classes, so the students are not required to see how to introduce this variable. 5. Explain why and how automatic stabilizers may be beneficial. The problems about active policy is: Policies act with long & variable lags, including: inside lag: the time between the shock and the policy response, takes time to recognize shock, takes time to implement policy, especially fiscal policy. outside lag: the time it takes for policy to a ect economy, If conditions change before policy s impact is felt, the policy may destabilize the economy. An automatic stabilizer, on the other hand, is designed to reduce the lags associated with stabilization policy. Question C Suppose the transition into unemployment is given by the rate s and the transition out of unemployment is equal to f. 3
1. Find the equilibrium unemployment rate u = U/L where U is unemployment and L is the labour force as a function of s and f. f U = s (L U), where L U is the number of employed workers. In equilibrium, at steady state, the number of workers finding a job, f L is equal to the number of workers losing a job all the time, s (L U). Collect terms to obtain: (f + s) U = sl and solve for the unemployment rate: u = U L = s s + f The unemployment rate increases with the separation rate, s, and falls with the job finding rate, f. 2. Let the job finding rate be equal to 0.3 and the separation rate be equal to 0.02. Find the equilibrium unemployment rate and explain verbally why the equilibrium unemployment rate is not equal to zero: u = U L = s s + f = 0.02 0.02 + 0.3 =0.0625 that is, 6.25 percent. As there will all the time be workers losing their jobs, it will never be equal to zero. 3. How would a firing cost a ect the equilibrium unemployment rate in this model. A firing costs would reduce s directly, making it more di cult for firms to fire a worker. This will therefore tend to reduce the unemployment rate. On the other hand, it will also reduce the job finding rate, as firms knowing that it is di cult to fire a worker will also hire fewer workers. This impact will then increase the unemployment rate. The impact on the unemployment rate is therefore ambiguous. 4. How does the equilibrium output level and the equilibrium unemployment level relate? Explain. A higher output level implies that firms employ more workers which reduces unemployment. Hence, higher output is related to lower unemployment. 5. Explain verbally and using an SRAS/LRAS-AD diagram how the economy approaches the equilibrium output level and thereby the equilibrium unemployment level if initially the unemployment rate is above its equilibrium/natural level because a negative demand shock has shifted the AD curve inwards. See Figure 4. The lower demand causes the price level to fall. But the price level is above the new clearing level. The SRAS moves down when the price level falls corresponding to an increase in real money 4
balances and thereby a downward shift of the LM curve. The interest rate therefore falls, which increases investment and hence demand for goods. This continues until the demand for goods again is equal to the long run supply of goods. The price level is now lower than before the shock. Question D 1. What are the assumptions needed to insure that the domestic interest rate is equal to the international determined interest rate, r = r. It has to be small open economy with perfect capital mobility (and no uncertainty). 2. Consider the long run. Show in a saving-investment and interest rate diagram the impact of expansionary fiscal policy abroad on the interest rate, net export, investment and saving and explain verbally. Expansionary fiscal policy abroad reduces world savings and thereby the world interest rate. Thereby the domestic interest rate increases. This has a negative impact on investment in the home country and therefore as domestic saving is given, implies an excess supply of loanable funds which corresponds to a higher net export. See Figure 5. 3. Explain how the result di ers when the expansive fiscal policy is only conducted in the home country. Expansive fiscal policy in the home country reduces saving and thereby reduces the supply of loanable funds which corresponds to a lower net export. See Figure 6. 5
Figure 1, Question A.3
Figure 2. Question A.4
Figure 4. Question C.5
Figure 5. Question D.2
Figure 6. Question D.3