102 Economics Introductory Macroeconomics Summer 2007, Professor Pavel Vacek
Problem Set 4
Due: on Wednesday, July 18
1. Why does the increase in government expenditure stimulate economy more than the same decrease of taxes? I.e. why is the tax multiplier (-b/1-b) smaller than the multiplier on autonomous expenditures (1/1-b)? [Technically because 0<=b<1 but this is not what I want, I want the intuition behind].
2. Consider the following information about a hypothetical open economy. (by open we mean that there are exports and imports, i.e. a foreign sector) planned I (I P) 50 50 50 50 50 50
Y 300 400 500 600 700 800
C 180 260 340 420 500 580
G 120 120 120 120 120 120
Taxes (T) 100 100 100 100 100 100
Exports 120 120 120 120 120 120
Imports 110 110 110 110 110 110
a) Assume that consumption function is linear, in the form: C(Y d)=a + b*(Y-T), where Yd=Y-T denotes disposable income, and "b" is the slope of the consumption function. Determine values of "a" and "b". b) What is the aggregate desired expenditure, AE d(Y)? c) What is the equilibrium level of national income, Y * ? d) Graph its determination in the "keynesian cross." e) What is the marginal propensity to consume? f) What is the marginal propensity to save? g) What is the value of the multiplier on autonomous expenditures? What does this multiplier tell us? h) What is the value of the tax multiplier (i.e. multiplier on taxes, T)? What does this multiplier tell us? i) Is this economy's budget balanced? j) What would happen to the equilibrium level of national income if planned investment (exogenously) increased by $2.5 billion? k) What would happen to the equilibrium level of national income if taxes (T) decreased by $2.5?
l) What would happen to the equilibrium level of national income if both government expenditures (G) and taxes (T) would be simultaneously increased by the same amount, say: G= T=+5 billion? m) What would happen to the equilibrium level of national income if government expenditures increased by $ 2.5 billion and simultaneously planned investment decreased by $ 1 billion?
3. You are given the following information about Isle de Cornell, a cold and snowy isolated island/country in the Finger Lakes, NY: Consumption function: C = 300 + 0.6Yd Planned investment: IP = 500 Government spending: G = 200 Taxes: T = 200 Exports EX= 100 Imports IM = 0.2Y, where 0.2 is the marginal propensity to import.
a) Determine the equilibrium level of national income of the Isle. b) What is the value of the keynesian multiplier on autonomous expenditures? c) What the is value of the tax multiplier? d) Fiscal policy: Suppose you are a king of Isle de Cornell (good luck!) and you want to increase its level of output (i.e. stimulate economic growth). Assume that Isle de Cornell has a substantial amount of unutilized resources. This means that an increase in expenditure (aggregate demand) will lead to an increase in output without inflation. You have several fiscal policy options: i) you may increase government expenditures (G), how will the equilibrium level of national income change if you increase G by 50? ii) ii) You may decrease taxes (T). How will the equilibrium level of national income change if you decrease T by 50? iii) Your dad taught you that you should not spend more money than you have, i.e. that as a king you should have your budget balanced. As a good son/daughter you decide to increase government expenditures and taxes simultaneously by the same amount to keep the budget balanced. If you simultaneously increase G by 10 and T by 10, how will the equilibrium income change?
4. You are given the following information about Ithaca. Consumption function: C = a + b(Yd), where Yd denotes disposable income, i.e. Yd=Y-T. Planned investment: IP = Ia Government spending: G = Ga Tax function T = Ta+tY, where Ta<0. Exports EX= EXa Imports IM = IMa [The subscript "a" indicates that the variables are autonomous, i.e. independent of income.] a) What is the form of the keynesian multiplier on autonomous expenditures? b) What is the form of the tax multiplier? Let us plug in numbers in our functions: Consumption function: C = 150 + 0.5Yd Planned investment: IP = 400 Government spending: G = 300 Tax function T = -200+0.25Y Exports EX= 50 Imports IM = 50
c) d) e) f)
What is the value of the keynesian multiplier on autonomous expenditures? What is the value of the tax multiplier? Determine the equilibrium level of national income in Ithaca. At the equilibrium level of national income, does Ithaca have a budget surplus or a budget deficit?
5. Assume some economy has a population of 100 people. Out of 140 people, there are: 10 soldiers, 20 people less than 16 years old, 20 college students, 5 people live in mental institutions, 2 are in prison, 3 are institutionalized in homes for aged, 15 are retired, 30 people are working, 10 are discouraged workers, 7 are homeless guys (they are not looking for jobs), 3 people are rich enough so they decided not to work and instead they go fishing everyday , and lastly there are 15 people without jobs but they are actively searching for it. What is the unemployment rate in this economy?