Answer:
a. Y = 500 - 20r
b. Y = 300 + 20r
c. r = 5; Y = 400
Step-by-step explanation:
a. Using the information above, derive the equation for the IS curve.
Y = C + I + G
Substituting for all the values, we have:
Y = 120 + 0.5(Y – 40) + 100 - 10r + 50
Y = 120 + 0.5Y - 20 + 100 - 10r + 50
Y - 0.5Y = 120 - 20 + 100 + 50 - 10r
(1 - 0.5)Y = 250 - 10r
0.5Y = 250 - 10r
Divide through by 0.5, we have:
Y = 500 - 20r <--------- IS curve Equation ............. (1)
b. Using the information above, derive the equation for the LM curve
M/P = L(r,Y)
Substitution for the values, we have:
600/2 = Y - 20r
300 = Y - 20r
Y = 300 + 20r <--------- LM curve Equation ............... (2)
c. What are the equilibrium levels of income and interest rate
Substitute Y in (2) into equation (1), we have:
300 + 20r = 500 - 20r
20r + 20r = 500 - 300
40r = 200
r = 200/40
r = 5 <--------- equilibrium level of interest rate .............. (3)
Substitute for r in equation (2), we have:
Y = 300 + 20(5) = 300 + 100
Y = 400 <--------- equilibrium level of income ................... (4)