. Suppose that the following equations describe an economy. (C, I,G, T and Y are
measured in billions of dollars, and r is measured as a percent; for example, r = 10 =
10%):
C = 170 + 0.6(Y − T)
T = 200
I = 100 − 4r
G = 350
(M/P)d
= L = 0.75Y − 6r
Ms
/P = M / P = 735
(a) Derive the equation for the IS curve. (Hint: It is easier to solve for Y here).
Solution: Y = 1250 – 10r
Suppose that the following equations describe an economy (C, I, G, T, and Y
are measured in billions of dollars and r is measured in percent; for example, r = 10
C=170+0.6(Y-T),T=200,I=100-4r,G=350
(M/P)d=L=0.75Y-6r, (M/P)s=735
a. Derive the equation for the IS curve (Hint: It is easier to solve for real output Y here)
b. Derive the equation for the LM curve (Hint: Again, it is easier to solve for real output
Y here)
c. Now express both the IS and LM equations in terms of r. Draw both curves and
calculate their slopes.
d. Use the equations from Parts a and b to calculate the equilibrium levels of real output Y,
the interest rate r, planned investment I, and consumption C.
e. At the equilibrium level of real output Y, calculate the value of the government budget
surplus.
f. Suppose that G increases by 36 to 386. Derive the new IS and LM equations and draw
these curves on the graph you drew for Part c.
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