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Chapter 22: Q 25. (page 583)

Suppose the MP curve is given by r=2+πand the IS curve is given by Y = 20 - 2r.

a. Derive an expression for the AD curve, and draw a graph labeling points at π=0,π=4,π=8

b. Suppose that λincreases to λ=2. Derive an expression for the new AD curve, and draw the new AD curve using the graph from part (a).

c. What does your answer to part (b) imply about the relationship between a central bank’s distaste for inflation and the slope of the AD curve?

Short Answer

Expert verified

(a) Y=16-2π

(b) Y=16-4π

(c) It has a more harmful affect on the output level.

Step by step solution

01

Step 1. Given information

The MP curve isr=2+π

The IS curve is Y=20-2r.

02

Step 2. Explanation

(a)

Combining the IS curve equation and the MP curve equation can provide the AD curve expression.

Y=20-2rY=20-2(2+π)Y=16-2π

The output level can be obtained as,

Y=16-2πAtπ=0,Y=16-2(0)Y=16Atπ=4,Y=16-2(4)Y=8Atπ=8,Y=16-2(8)Y=0

03

Step 3. Explanation Part (b)

(b)

The new AD curve expression would be,

Y=16-4π

The output level can be obtained as,

Atπ=0Y=16-4(0)Y=16Atπ=4,Y=16-4(4)Y=0

04

Step 4.Explanation Part (c)

It shows a negative relationship between the slope of the AD curve and the responsiveness of the real interest rate to inflation rate. When the inflation rate increases along with an increase in λit has a more harmful affect on the output level.

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Most popular questions from this chapter

What would be the effect of an increase in U.S. net exports on the aggregate demand curve? Would an increase in net exports affect the monetary policy curve? Explain.

A measure of real interest rates can be approximated by the Treasury Inflation-Indexed Security, or TIIS. Go to the St. Louis Federal Reserve FRED database, and find data on the five-year TIIS (FII5) and the personal consumption expenditure price index (PCECTPI), a measure of the price index. Choose “Quarterly” for the frequency setting of the TIIS, and download both data series. Convert the price index data to annualized inflation rates by taking the quarter-to-quarter percent change in the price index and multiplying it by 4. Be sure to multiply by 100 so that your results are percentages.

a. Calculate the average inflation rate and the average real interest rate over the most recent four quarters of data available and the four quarters prior to that.

b. Calculate the change in the average inflation rate between the most recent annual period and the year prior. Then calculate the change in the average real interest rate over the same period.

c. Using your answers to part (b), compute the ratio of the change in the average real interest rate to the change in the average inflation rate. What does this ratio represent? Comment on how it relates to the Taylor principle.

Assume that the monetary policy curve is given by

r = 1.5 + 0.75p.

a. Calculate the real interest rate when the inflation rate

is 2%, 3%, and 4%.

b. Draw a graph of the MP curve, labeling the points

from part (a).

c. Assume now that the monetary policy curve is given

by r = 2.5 + 0.75p. Does the new monetary policy

curve represent an autonomous tightening or loosening

of monetary policy?

d. Calculate the real interest rate when the inflation rate

is 2%, 3%, and 4%, and draw the new MP curve,

showing the shift from part (b).

Why does the MP curve necessarily have an upward slope?

Suppose that a new Fed chair is appointed and that his or her approach to monetary policy can be summarized by the following statement: "I care only about increasing employment. Inflation has been at very low levels for quite some time; my priority is to ease monetary policy to promote employment." How would you expect the monetary policy curve to be affected, if at all?
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