Consider an economy described by the following equations: C = 250 + 0.75(Y ? T )
ID: 1152943 • Letter: C
Question
Consider an economy described by the following equations: C = 250 + 0.75(Y ? T ) I = 750 G = 1000 T = 1000 N X = 0 (For each of the questions below make sure you understand conceptually why you get the answersthat you do, even though you’re not always asked to explicitly explain why.) (a) Find equilibrium GDP (Y ) and consumption (C) in thiseconomy. (b) Now suppose that the government cuts spending to G = 900 and cuts taxes to T = 900. What is the new equilibrium GDP? (Make sure to understand why it went up or down in this model.) (c) Returning to the original specification (ignoring changes from part (b)), suppose that people want to save less so the marginal propensity to consume rises from 0.75 to 0.8. What is the new equilibrium GDP? What is the new equilibrium level of consumption?
Explanation / Answer
a) Y = C + I + G + NX
Y = 250 + 0.75(Y - T) + 750 + 1000 + 0
Y = 250 + 0.75(Y - 1000) + 1750
Y = 2000 + 0.75Y - 750
0.25Y = 1250
Y = 5000
C = 250 + 0.75(5000 - 1000) = 250 + 0.75 x 4000 = 250 + 3000 = 3250
b)
Y = C + I + G + NX
Y = 250 + 0.75(Y - T) + 750 + 900 + 0
Y = 250 + 0.75(Y - 900) + 1650
Y = 1900 + 0.75Y - 675
0.25Y = 1225
Y = 4900
c)
Y = C + I + G + NX
Y = 250 + 0.8(Y - T) + 750 + 1000 + 0
Y = 250 + 0.8(Y - 1000) + 1750
Y = 2000 + 0.8Y - 800
0.2Y = 1200
Y = 6000
C = 250 + 0.8(6000 - 1000) = 250 + 0.8 x 5000 = 250 + 4000 = 4250