ECON1102 Lecture Notes - Lecture 10: Real Interest Rate, Aggregate Demand, Best Response

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18 May 2018

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10 – Aggregate Demand and Aggregate Supply

PAE and real interest rate

• In income-expenditure model, PAE depends on level of real output

 Want to allow for the real interest rate to influence PAE

• Two main channels:

1. Higher real interest rates will lead households to increase saving and defer

current consumption

2. Higher real interest rates will raise the cost of capital and reduce business

investment

Model for PAE

• Consumption: C = C0 + c (Y – T) – r

• Investment: IP = I0 – ßr

 (–) is negative effect from real interest rate

 Assume  > 0 and ß > 0 are some positive numbers

• PAE = [C0 – cT0 + I0 + G0 + X0] – ( + ß)r + (c (1 – t) – m)Y

 PAE depends (negatively) on real interest rate

 For any given output level, PAE will fall with an increase in the real interest rate

 If we assume that the RBA can set the real interest rate, then we have a

mechanism by which monetary policy can affect PAE and equilibrium output

• Y = PAE:

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• Mechanism by which monetary policy can affect real GDP

Policy reaction function

• r = r0 + yπ

 y > 0 captures the (endogenous) response of the RBA to inflation

 r0 represents factors – other than inflation rate – that might influence real policy

rate

(a) Changes in r0 reflect discretionary changes in monetary policy

Aggregate demand (AD) curve

• A PAE curve that depends on the real interest rate

• A policy reaction function for the RBA, in which the real interest rate responds to the

inflation rate

• PAE curve & PRF → AD curve

 Link output Y and inflation π

• Simplifying:

 Let k =

• Model implies a negative relationship between equilibrium output and rate of

inflation

AD curve has a negative slope

• Other things equal, an increase in inflation is associated with a fall in equilibrium

output

• Model explains negative slope as reflecting behaviour of central bank

• When inflation is high, RBA will raise real interest rate

 Increase in r reduces consumption and investment (i.e. PAE) and this produces a

fall in equilibrium output

• Other reasons not explicitly stated in model: wealth, distributional and uncertainty

effects

Shifts in AD curve

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• Exogenous changes in spending or taxes

 Fiscal policy, private spending

• Eogenous change in RBA’s polic reaction function, r0

 Increase in r0 produces an upward shift in the PRF (tighter monetary policy) and

leads to inward shift in AD curve

Aggregate supply – how does inflation change with aggregate production?

• Expected rate of inflation

 Assume expected & actual inflation is sticky or slow to adjust in the short-run

(a) Consistent with observed persistence in inflation rates

i. Actual = expected inflation: π = πe

ii. Adaptive expectations: πe = π-1

iii. Actual inflation: π = π-1

(b) Inflation is constant (fixed or sticky) in short-run

• Aggregate shocks to business production costs

 Introduce one-period shocks to inflation rate (e.g. indirect tax changes or

changes in energy prices)

 π = π-1 + 

(a)  > 0 = adverse or unfavourable shock

(b)  < 0 = favourable shock

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Document Summary

In income-expenditure model, pae depends on level of real output. Model for pae: consumption: c = c0 + c (y t) r. ( ) is negative effect from real interest rate. Assume > 0 and > 0 are some positive numbers: pae = [c0 ct0 + i0 + g0 + x0] ( + )r + (c (1 t) m)y. Pae depends (negatively) on real interest rate. For any given output level, pae will fall with an increase in the real interest rate. Policy reaction function r = r0 + y . Y > 0 captures the (endogenous) response of the rba to inflation. R0 represents factors other than inflation rate that might influence real policy rate (a) changes in r0 reflect discretionary changes in monetary policy. Link output (cid:894)y(cid:895) and inflation (cid:894) (cid:895: simplifying: Let k : model implies a negative relationship between equilibrium output and rate of inflation.

Related Questions

C = 1275 + 0.5(Y-T) â 200r

I = 900 â 200r

Real Money demand, L = 0.5Y â 200i

Expected inflation, ? = 0

Full employment output, = 4600

a.) Suppose that T = G = 450 and M = 9000

Find an equation describing the IS curve

Find an equation describing the LM curve

Find an equation for the aggregate demand curve (Hint: Use IS and LM equations to find a relationship between Y and P)

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

b) Suppose M = 4500, T and G remain the same.

What is the equation for the aggregate demand curve?

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

c.) Suppose T = G = 330 and M = 9000

What is the equation for the aggregate demand curve?

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

orchidsardine515

A Keynesian economy is described by the following equations :

C^d = 250 + 0.5(Y - T) - 250r

I^d = 250 - 250r

G = 300

T = 300

L = 0.5Y - 500r + Ï^e

M = 3000

Y = 1250

Ï^e = 0

a) Calculate the values of the real interest rate, the price level, consumption, and investment for the economy in general equilibrium.

(b) Now suppose government purchases increase to 350 with no change in taxes. What will be the real interest rate, the price level, output, consumption, and investment in the short run?

sangriamink160

Monetary Policy and Inflation: Use our standard Keynesian macroeconomic model:

â¢ Y = E = C + I + NX + G â GDP equals the sum of consumption, investment, net exports, and government purchases
â¢ C = c0 + cy x Y â consumption equals the consumer-confidence term plus the mpc times GDP or income
â¢ I = I0 - Ir x r â business investment spending equals the business animal-spirits term minus the interest sensitivity of investment times the long-run real risky interest rate
â¢ Î¼ = 1/(1 - cy) â the multiplier is the inverse of one minus the mic
â¢ Y = Î¼(c0 + I0 + NX) - (Î¼ Ir) x r + Î¼G â our summing-up equation, telling us how the level of annual GDP depends on the multiplier Î¼, on the private spending flows c0 + I0 + NX, on the
interest-sensitivity parameter Ir, on the interest rate r, and on government purchases G

For this problem, assume a value of the Keynesian multiplier of Î¼ = 2, and with Ir, the sensitivity of investment spending I to the interest rate r, such that Ir = $0.15T. And letâs use the Greek letter Îâcapital deltaâas a shorthand symbol for changes from the previous equilibrium situation.

The Federal Reserve controls the short-term safe interest rate on government securitiesâit can nail that value to whatever it wants by buying and selling bonds for cash. We call this interest rate i. But the interest rate that matters for determining investment spending is the long-term real risky interest rate at which banks lend to companies. We call this interest rate r.

a) Suppose that the interest rate r that matters for investment spending falls by 1.5%-pts:
Îr = -1.5
By how much would you expect investment spending to fall given the parameter values of our model? How large is ÎI?

b) Continue your analysis from (a): given the parameter values of our model and the boosting of investment spending you calculated in (a), by how much would you expect GDP Y to grow?

c) Annual real GDP in the mid-2000s was about $15T. How large is this boost to GDP ÎY you calculated in (b) as a percentage of the then-level of real GDP?

d) On average, a 1% extra boost to GDP is associated with a 1.5% extra decrease in the unemployment rate. By how much extra would you expect the unemployment rate to fall as a
result of the boost to GDP you calculated in (b) and (c)?

e) Suppose that with the interest rate decline the unemployment rate falls from 6% to 4.5%. What would the unemployment rate have been without this interest-rate decline?

f) Suppose that real GDP had been lower for each of three years by the amount you calculated in (b). How much poorer would Americans have been in terms of reduced income over those three years had the interest rate r not fallen?

g) In an America with about 135 million workers, how much is this lost income per worker?

ochredonkey719

ECON1102 Lecture Notes - Lecture 10: Real Interest Rate, Aggregate Demand, Best Response

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