1. Assume that the equilibrium in the money market may be described as M/P = 0.5
ID: 1187358 • Letter: 1
Question
1. Assume that the equilibrium in the money market may be described as M/P = 0.5Y - 100r, and M/P equals 800.
a. Write the LM curve two ways, expressing Y as a function of r and r as a function of Y. (Hint: Write the LM curve only relating Y and r; substitute out M/P.)
b. What is the slope of the LM curve?
c. If r is 1 percent, what is Y along the LM curve? If r is 3 percent, what is Y along the LM curve? If r is 5 percent, what is Y along the LM curve?
d. If M/P increases, does the LM curve shift upward and to the left or downward and to the right?
e. If P increases and M is constant, does the LM curve shift upward and to the left or downward and to the right?
Explanation / Answer
a) M/P = 800
Writing LM curve : Y as a function of r
0.5Y = M/P + 100r
0.5Y = 800 + 100r
Y= 200r + 1600 ---> Y as a function of r - (1)
Now writing it as r as a function of Y
100r = 0.5Y - M/P
100r = 0.5Y - 800
r= 0.005Y - 8 ----> r as a function of Y - (2)
b) LM curve is usually represented in this form : Y as a function of r i.e Y = mr + c where m is the slope and c is the intercept
Y = 200r + 1600 from (1)
Hence the slope of the LM cure is 200
c) if r =1% , substitute in (1) r = 0.01 we get y as 1602
if r = 3% Y = 1606
if r = 5% Y = 1610
d) M/P reprents the Y intercept of the LM curve, hence if M/P increases, the intercept increases and the LM curve shifts upward and to the left.
e) if P increases and M is constant, the value of M/P decreases and hence the Y intercept decreases, hence the LM curve shifts downward and to the right.
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