Mathematical Model of AD 1. Suppose the following information reflects the close
ID: 1182860 • Letter: M
Question
Mathematical Model of AD 1. Suppose the following information reflects the closed economy of Casolari Land. The Consumption Function is such that C=300+.75(DI), Investment is fixed at $450 and the Government has a balanced budget, where both purchases and taxes equal $1,000. (a) Calculate the equilibrium level of GDP for this economy (Y*). (b) Assume the Potential level of output is $5,000, what action can the government take, if any? (Hint: There are three policy tools available. Describe each.) (c) Suppose the government chooses to increase itExplanation / Answer
First, we must express AE as the sum of all expenditures from the list of equations above. This implies writing out AE as AE = C + I + G + X - M, and then substituting everything into its appropriate spot in that equation. AE = C + I + G + X - M AE = [0.75(DI) + 400] + 1200 + 1600 + 500 - 600 Remembering that DI = Y - T, where Y = real GDP, we have: AE = [0.75(Y - T) + 400] + 1200 + 1600 + 500 - 600 AE = [0.75(Y - 1200) + 400] + 1200 + 1600 + 500 – 600 AE = 0.75Y + 2200 This equation tells us how expenditure changes when people’s income changes. For example, if we wanted to forecast how much (aggregate) expenditure would occur when GDP is $20,000, then we can just plug $20,000 into that equation for Y and solve. The answer would be that AE = $15,000 when Y = $20,000. Remember, however, that our goal is to find the point where this economy is at equilibrium. We will then compare the GDP that occurs at equilibrium to the GDP we get at full employment (i.e. Potential GDP) and ask how to close any output gap that might exist. When an economy is in equilibrium, the overall amount of expenditures will equal the total value of output produced (i.e. final goods and services produced in a given period). Within the AE model, the model we’re working with here, equilibrium would occur when AE = Y. Therefore, we only need to substitute Y for AE in the equation above. Y = 0.75Y + 2200 We now must ask what Y (real GDP) must be in order for this equation to be true. That is, what must Y be in order for Y to equal 0.75Y + 2200? We can use algebra to solve for that answer as follows: Subtract 0.75Y from both sides and simplify Y - 0.75Y = 0.75Y - 0.75Y + 2200 0.25Y = 2200 Divide both sides by 0.25 and simplify 0.25Y/0.25 = 2200/0.25 Y = 8800 That is, equilibrium real GDP (Y*) is equal to 8800. Given that Potential GDP is equal to 9000, we calculate the amount of the output gap as the difference between equilibrium GDP and potential GDP. In doing so, we find that there is an output gap of 200 (i.e. Yp - Y* = 200).