Download GNP Problem

Economics 101, Queens College MOST IMPORTANT HOMEWORK TO UNDERTAND
Prof. Michael R. Dohan
Spring 2011
SIMPLE ALGEBRAIC GDP EQUILIBRIUM PRACTICE PROBLEM
(Show your work or explain or illustrate how you find the answers and the principles involved.)
As an economic adviser to a large industrial nation, you have the following information about the
economy (billions of dollars in constant prices per year). Assume no corporate saving.
Consumption Behavior
Investment Behavior
Government Spending
Disposable Income
Taxes and Transfer Policy
Exports
Imports
Aggregate Demand or planned expenditure
Equilibrium Condition
Cd = 225 + .75Ydi where .75 equals MPC
Id = 200 (no induced investment)
Gd = 500
Ydi = Ya - Tx + TR
Tx = 500, TR = 400
X = 200
M = 400
Yd = C + I + G +(X-M)
Y*a = Yd where Ya is GDP output
Using both the algebraic approach and the graphic approach, answer the following questions.
1.
What is the aggregate demand function?
Yd = C + I + G
+ X-M
(definition)
2. What is the equilibrium of GDP? (i.e., denoted by symbol Y*a)
(show your work)
Now substitute value or equations in for symbols to get our estimate of aggregate demand as a
function of output. Yd = 225 + .75*Ydi +200 + 500 +200 -400
Now we substitute in our definition of disposable income, so we get
Yd = 225 + .75*(Ya-Tx+Tr) +200 + 500 +200 -400 and again for Tx = 500 & Tr = 400,
Yd = 225 + .75*(Ya-500 + 400) +200 + 500 +200 -400 .
Now we “distribute” the MPC = .75 over the elements defining disposable income and we get
Yd = 225 + .75*Ya- .75*500 + .75* 400 +200 + 500 +200 -400
Which simplifies to Yd= +.75*Ya +225 – 375 + 300 + 200 +500 +200 -400
Aggregate demand Yd =
C
+ I +G +X - M
So now we have two equations and two unknown. The other equation is the definition of
equilibrium: Ya = Yd where Ya is GDP output and
Set Ya = Yd remembering that Ya has the coefficient “1” in front of it.
Solve for Ya by setting Ya equal to Yd
Ya= +.75*Ya +225 – 375 + 300 + 200 +500 +200 -400
Substract .75Ya from both sides
1Ya-.75Ya = +.75Ya-.75Ya + 225 – 375 +300 + 500 + 200 - 400
(1-.75) Ya =
+ 225 – 375 +300 + 500 + 200 – 400
Multiply both sides by 1/(1-.75)
1/(1-.75)*(1-.75)Ya = (1/(1-.75 ))*( 450) => 1Ya = (1/(1-.75 ))*( 450)
Y* a =
4 * 450
= 1800
3. What is the MPC and what is the multiplier? MPC = .75 Multiplier = (1/(1- .75) = 4
Graphic answer in on next page
Upward shift in ∆Yd
Full employment = 300
Ya
Yd = C+I + G+ X
Yd = C+I + G+ X - M
M = 400
X = +200
G = +500
I = +200
Cut in G to eliminate
budget deficit = 400
Full employment = 300
Y*a = =1800
225
∆Ya*=-1600
Depression
Anti Deficit
Policy =200
Y*a=
1800
∆Ya*=+1200
Full Employment
Full employment output
Y*a =30000
Yfe=
3000
DO EACH OF THE FOLLOWING PROBLEMS USING THE ORIGINAL PROBLEM.
Show all your work. Label each question carefully.
4. Assume full employment level of GDP (YFE) is 3000 billion dollars. Calculate and sketch a graph on a
separate piece of graph paper, that shows graphically what type and how much of a "gap" exists.
(Inflationary or Recessionary Gap) . In words, what type of articles would you expect to read in the Wall
Street Journal, etc.
Deflationary, unemployment,
5.
Would the Republican policy to reduce the deficit to balance the budget be a good policy to reach full
employment with price stability. The deficit is currently D= Tx – G – Tr = 500 -500 – 400 = -400
If we shift the Yd (the aggregate demand function) down by ∆Yd= 400, ceteris paribus, change in the
equilibrium level ∆Y* = M * ∆Yd = 4 * -400 = 1600 and we would have catastrophic decline in output
and employmen into the great depression. The British are suffering a mild version of that now.
6. What changes in Gd will shift equilibrium GDP (Y*a) to YFE?
We need to raise Y*a by 1200 from 1800 to 3000. ∆Ya*=+1200,
but since M x (upward shift in ∆Yd) will equal ∆Ya*, so that (needed ↑ ∆Yd) will equal ∆Ya*/M,
so 1200/4 = 300 so ∆Yd only is 300, the rest of the expansion comes from the multiplier effect or the
secondary expansion of consumption. An increase in G increases Yd dollar for dollar.
7. What changes in Tx will shift equilibrium GDP to YFE?
Changes in taxes (& transfers) work differently. Remember the change in consumption from a change taxes
or transfers works through disposable income. ∆C= mpc* ∆Ydi and that ∆Ydi = -∆Tx +∆TR
So that ∆C = mpc * (-∆Tx +∆TR ). What is the mpc? MPC = .75. What change in consumption so
we need to start the expansion. ∆Yd only is 300. So we need an increase in consumption of only 300.
But we have to CUT taxes or INCREASE transfer payments by 400,. Why? Because households
response to a change in disposable income by changing savings too. So to increase consumption by 300
we need to increase disposable income by 400 => 300 for increased consumption and 100 for increased
saving. SO!! Focusing just on taxes for this example:
∆Tx = (-1)∆C/mpc => (-1)*(300)/.75 = -400. Why (-1)? Because you have to cut taxes to raise Ydi.!
Ydi moves the opposite direction of taxes and the same direction as transfer payments.