Macroeconomics Answer Note #4

Question 1 . By raising aggregate demand more than anticipated, policymakers a. raise unemployment permanently. b. reduce unemployment permanently. c. raise unemployment temporarily. d. reduce unemployment temporarily. the correct answer is Answer The correct answer to this question is option d: reduce unemployment temporarily. This is because an increase in aggregate demand leads to an increase in economic activity, which in turn creates job opportunities and reduces unemployment in the short term. Question 2 Given the following information for a closed economy: Consumption C=100 +0.8Y; Investment I=1200-30r (r is the interest rate), Precautionary and Transaction Demand for Money L(Y)=-0.25%; Speculative Demand for Money L(r)=1375-25r, and Money Supply, MS= 2500. 1) Find the equilibrium value of Y and r 2) What property is shared by all points along the LM schedule? 3) What property is shared by all points along the IS schedule? 4)Explain why the IS curve is negatively sloped in the IS-LM curve model 5)Explain why the LM curve is positively sloped in the IS-LM model 6)What factor(s) indicate whether the slope of the IS curve is steep or fiat? 7)What factor(s) indicate whether the slope of the LM curve is steep or flat? Answer 1) To find the equilibrium value of Y and r, we need to set the aggregate demand (AD) equal to the aggregate supply (AS), that is, C+I+G+NX = Y. In a closed economy, there is no NX (net exports) term, and G (government spending) is assumed to be constant. Therefore, the equilibrium condition becomes C+I = Y. From the given information, we can rewrite C and I as functions of Y and r: C=100+0.8Y and I=1200-30r. Substituting these into the equilibrium condition, we get 100+0.8Y+1200-30r = Y. Rearranging, we get 100+1200 = Y-0.8Y+30r, which simplifies to 1300 = 0.2Y+30r. From the money demand function, L(r) = 1375-25r, we can also rewrite the equation as 1300 = 0.2Y+30(L(r)/25). Substituting the given monetary supply (MS=2500) for the monetary demand, we get 1300 = 0.2Y + 1200 - 6L(r). Finally, substituting the precautionary and transaction demand function (L(Y)=-0.25%) for L(r), we get 1300 = 0.2Y + 1200 - 6(-0.25%Y). Solving for Y, we get Y = 13000. Therefore, the equilibrium value of Y is 13000. To find the equilibrium value of r, we can substitute the equilibrium value of Y into the money demand function (L(r) = 1375-25r). This gives us 1300 = 1375 - 25r. Solving for r, we get r = 3. For the given information, the equilibrium value of r is 3. 2) The property shared by all points along the LM schedule is that they all represent the combinations of r and Y that equate money supply (MS) to money demand (MD). This means that for any point on the LM schedule, the quantity of money demanded will equal the quantity of money supplied, leading to an equal intersection point between MS and MD. 3) The property shared by all points along the IS schedule is that they all represent the combinations of r and Y that equate investment (I) to national saving (S). This means that for any point on the IS schedule, investment will equal national saving, leading to an equal intersection point between I and S. 4) The IS curve is negatively sloped in the IS-LM curve model because of the inverse relationship between interest rates and investment. As the interest rate (r) increases, the cost of borrowing increases, leading to a decrease in investment. Therefore, as r increases, investment decreases, causing a downward sloping IS curve. 5) The LM curve is positively sloped in the IS-LM model because of the direct relationship between income (Y) and money demand. As income increases, so does the demand for money, leading to an increase in the interest rate (r) to maintain equilibrium in the money market. Therefore, as Y increases, r increases, causing an upward sloping LM curve. 6) The slope of the IS curve depends on the magnitudes of investment and national saving. If investment is a large portion of GDP, the slope of the IS curve will be steeper. This is because investment has a larger impact on GDP, and therefore, changes in the interest rate will have a bigger effect on the level of output. On the other hand, if national saving is a large portion of GDP, the slope of the IS curve will be flatter. This is because changes in the interest rate will have a smaller effect on investment and therefore, a smaller impact on output. 7) The slope of the LM curve depends on the sensitivity of money demand to changes Question 3 Given the identity of an open economy, Y=C+I+G+X-M, where C=a+bYd, Yd=Y-T and T= t0+t1Y, H=ho-h1r and M=m0+m1Y. You are required to 1) Derive the equilibrium level of Y. 2) Obtain the value of Y, if C=130+0.75Y, T=30+0.15Y, I=250-500r, M=300+0.55Y, G=750, X=1020, r=20% 3) Compute the value of tax-trade multiplier in the economy. 4) Assuming government decides to operate a balanced budget by charging a lump-sum tax, T=150. What is the new equilibrium level of income? 5) Explain how transfer payment by government to consumers will affect the equilibrium level of national income. Answer Given the identity of an open economy, Y=C+I+G+X-M, where C=a+bYd, Yd=Y-T and T= t0+t1Y, H=ho-h1r and M=m0+m1Y: 1) Deriving the equilibrium level of Y: To derive the equilibrium level of Y, we need to set Y=C+I+G+X-M equal to itself. This means that Y will equal all the components added together. Using the equation for Yd and T, we can rewrite the equation as Y = a + b(Y- T) + I + G + X - M. This can be further simplified to Y = a + bY -bT +I + G + X - M. We can then substitute the equation for T (t0 + t1Y) in place of T, giving Y= a + bY -bt0 -bt1Y + I + G + X - M. We then bring the terms with Y to one side and the remaining terms to the other side, giving Y bY + bt1Y = a -bt0 + I + G + X - M. We can then factor out Y to give Y(1-b + bt1) = a bt0 + I + G + X - M. Finally, we can divide both sides by (1-b+bt1) to get the equilibrium level of Y: Y = (a - bt0 + I + G + X - M)/(1-b+bt1). 2) Obtaining the value of Y: To obtain the value of Y, we can simply plug in the given values for C, T, I, M, G, and r into the equation we derived in part 1. This gives us Y = (130+0.75Y) + (30+0.15Y) + (250-500(0.20)) + (300+0.55Y) + 750 + 1020 - (0.20Y). Simplifying this equation gives us Y = 730 + 5.90Y - 100 - 100 + 1.1Y + 750 + 1020 - 0.20Y. We can then combine like terms to get 6.80Y = 3300, giving us the value of Y= 3300/6.80= $485.29 billion. 3) Computing the value of tax-trade multiplier: To compute the value of tax-trade multiplier, we need to use the formula for Y with the tax multiplier. The formula for the tax-trade multiplier is equal to -b/(1-b+bt1). Using the given values for b and t1, we can plug them in to get the tax-trade multiplier = -0.75/(10.75+0.75(0.15)) = -0.75/1.1125 = -0.674. This means that for every 1% change in taxes, the equilibrium level of Y will drop by 0.674%. 4) Calculating the new equilibrium level of income: Assuming the government decides to operate with a balanced budget by charging a lumpsum tax of T=150, we can use the equation derived in part 1 to calculate the new equilibrium level of income. This gives us Y = (a - bt0 + I + G + X - M + T)/(1-b+bt1). Substituting the given values for a, b, t0, t1, I, G, X, M, and T, we get Y = (130-0.75(30)100+250-500(0.20)+750+1020-300+150)/(1-0.75+0.75(0.15)) = $466.67 billion. 5) Explaining the effect of transfer payments on the equilibrium level of national income: Transfer payments from the government to consumers refer to any payments made by the government to individuals or families for which no goods or services are required in return. Examples include social security payments, welfare, and unemployment benefits. Transfer payments are not included in the government spending component (G) in the equilibrium equation, but they do have an indirect effect on national income through their impact on consumption (C). When transfer payments increase, they provide individuals with additional income which they can use to consume goods and services. This leads to an increase in consumption (C), causing aggregate demand to shift to the right, which in turn increases the equilibrium level of national income. On the other hand, if transfer payments decrease, it will lead to a decrease in consumption, causing a decrease in the equilibrium level of national income. Question 4 For the following economy, find autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap. By how much would autonomous expenditure have to change to eliminate the output gap C = 3000 + 0.5 (Y-T) IP = 1500 G = 2500 NX = 200 T = 2000 Y* = 12000 1) Autonomous expenditure = ? 2) Multiplier = ? 3) Shortrun equilibrium output = ? 4) Output gap = ? 5) Autonomous expenditure would need to _____ by ____ to eliminate the output gap. Answer In this question, we are given a set of variables representing the components of aggregate demand in an economy; Consumption (C), Investment (I), Government spending (G), Net exports (NX), Taxes (T), and potential output (Y*). The equation for autonomous expenditure is C + I + G + NX, which are all represented in the given variables. The goal of this question is to calculate the values for autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap, and determine how much autonomous expenditure would need to change to eliminate the output gap. 1) Autonomous expenditure: To calculate autonomous expenditure, we need to substitute the given values into the equation C + I + G + NX. This gives us: C = 3000 + 0.5(Y-T) = 3000 + 0.5(12000-2000) = 9000 I = 1500 G = 2500 NX = 200 Therefore, autonomous expenditure = 9000 + 1500 + 2500 + 200 = 13200 2) Multiplier: The multiplier in this economy can be calculated using the formula 1/(1-MPC), where MPC (Marginal Propensity to Consume) is the change in consumption for every change in income. In this case, MPC = 0.5. Thus, the multiplier = 1/ (1-0.5) = 2. 3) Short-run equilibrium output: To find the short-run equilibrium output, we need to equate aggregate demand (AD) with the potential output (Y*) in the given economy. This can be represented as AD = C + I + G + NX = Y*. Substituting the values from the given variables, we get: 9000 + 1500 + 2500 + 200 = Y* Y* = 13200 4) Output gap: The output gap is a measure of the difference between actual output and potential output. In this case, the potential output is 12000, and the actual output is 13200. Therefore, the output gap = 13200 -12000 = 1200. 5) Change in autonomous expenditure to eliminate output gap: To eliminate the output gap, we need to bring the actual output (13200) to equal the potential output (12000). Since autonomous expenditure is a component of aggregate demand, we need to increase it by the amount of the output gap (1200). Therefore, autonomous expenditure would need to increase by 1200 to eliminate the output gap. Question 5 is an increase in budget deficit considered as aggregate demand or aggregate supply or both? give definition, explain and explain where it shifts Answer According to Keynesian economics, an increase in budget deficit is considered as an increase in aggregate demand. Aggregate demand is the total amount of goods and services that an economy plans to buy at different price levels. With an increase in budget deficit, the government is essentially injecting more spending into the economy, either through increased government spending or tax cuts. This increase in spending will lead to an increase in aggregate demand, as consumers will have more disposable income to spend and businesses will see a rise in demand for their products and services. This will, in turn, lead to an increase in overall economic activity and output. However, some economists argue that an increase in budget deficit can also lead to a decrease in aggregate supply. This is because government spending often leads to inflation, which can make it difficult for businesses to supply goods and services at affordable prices. Additionally, if the government is borrowing excessively to finance the budget deficit, it can lead to higher interest rates, which can discourage investment and hinder economic growth. In summary, an increase in budget deficit has both demand-side and supply-side effects, but overall it is seen as a boost to aggregate demand. It is important for policymakers to carefully manage budget deficits to strike a balance between stimulating the economy and maintaining a sustainable level of debt.