Chapter 13
Aggregate Supply and the Short Run Tradeoff Between Inflation and Unemployment
Basic Theory of Aggregate Supply
Inflation, Unemployment, and the Phillips Curve
2 models of aggregate supply
Sticky-price model
Imperfect-information model
Both models imply (AS equation)
Sticky-price causes
long-term contracts betweens firms/customers
menu costs of changing prices
firms don't want to annoy customers with frequent price changes
Assumption: firms set their own prices (have some market power/ability to influence prices)
An individual firm's desired price
Y = Ybar + b(P - EP)
Y = aggregate output
Ybar = natural level of output
b = positive parameter, (s/(1-s)a)
P = price level
EP = expected price level
p = P + a(Y - Ybar)
p = price of individual firm
P = overall price level
a = a positive parameter
Y = aggregate output
Ybar = natural level of output
Firm's desired price of its product depends on
Price level: Affects both
Level of aggregate output relative to Y(bar)
When economy is weak, firms set prices lower
nominal price charged by competitors
nominal price cost of inputs
When demand is high, firm set higher prices
2 types of firms
Flexible price firms: set price according to p = P + a(Y - Ybar)
Sticky price firms: set their price before they know how P and Y will turn out. Use p = EP + a(EY - EYbar), or p = EP (assume Ybar expected)
Equation for overall price level
P = s [EP] + (1-s) [P + a(Y - Ybar)]
s = fraction of firms with sticky prices
[EP] = price set by sticky firms
[P + a(Y - Ybar)] = price set by flexible firms
Subtract (1-s) from both sides to get:
P = EP + (((1-s)a) / s) (Y - Ybar), or
Y = Ybar + b(P - EP)
b = (s/(1-s)a)
High EP means high P (flexible firms will set high price too)
High Y means high P (income high means demand is high, meaning high prices (impact greater if more flexible firms))
Assumptions
Wages and prices flexible, markets are clear
Each supplier produces one good, consumes many goods
Each supplier knows nominal price of their own good, but not over all price
Supply of each good depends on relative price of good compared to different goods. Relative price: nominal price of good divided by overall price level
Supplier does not know price level when she makes production decision, so uses EP
Suppose P rises
But EP does not, P > EP
With many producers thinking this way, Y will rise whenever P rises above EP.
But supplier expects this, EP = P
Supplier thinks her relative price has risen, so she produces more (thinks money earned from each additional product allows her to buy more goods)
When
P = EP, Y = Ybar
P > EP, Y > Ybar
P < EP, Y < Ybar
Phillips Curve
Ο = EΟ - π(u - un) + π
Ο = inflation
EΟ = expected inflation
π = exogenous value, π > 0
u = unemployment
un = natural level of unemployment
π = supply shock
(u - un) = cyclical unemployment: the deviation of unemployment from its natural rate
Derive Phillips curve from SRAS (7)
Comparing SRAS and Phillips Curve
Disinflation
Adaptive vs Rational Expectations
Okun's Law
(1) Y = Ybar + b(P - EP)
(2) P = EP + 1/b (Y - Ybar)
(3) P = EP + 1/b (Y - Ybar) + π
(4) (P - P-1) = (EP - P-1) + 1/b (Y - Ybar) + π
(5) Ο = EΟ + 1/b (Y - Ybar) + π , Ο (%) is not exactly (P - P-1)
(6) 1/b (Y - Ybar) = -π(u - un) , π>0
(7) Ο = EΟ - π(u - un) + π
SRAS
Phillips curve
Output is related to unexpected movements in the price level
Y = Ybar + b(P - EP)
Ο = EΟ - π(u - un) + π
Unemployment is related to unexpected movements in the inflation rate
People adjust expectations over time, so tradeoff only works in the short run, before the new Ο becomes EΟ and we are back at natural levels of unemployment.
Sacrifice Ratio
Deviation of output from its natural rate is inversely related to cyclical unemployment (unemployment rate vs GDP)
The percentage of a year's real GDP that must be sacrificed to reduce inflation by 1 percentage point (inflation vs GDP)
1 percentage point in unemployment rate = 2 percentage point GDP
1 percentage point in inflation = 2 to 5 percentage point in GDP
1 percentage point in inflation = 1 to 2.5 percentage point in unemployment rate (or cyclical unemployment)
Disinflation could take various forms, e.g. the same sacrifice over 1 year vs over 10 years.
GDP loss = inflation reduction * sacrifice ratio
Sacrifice ratio = lost GDP / total disinflation
Adaptive expectations: People form their expectations of future inflation based on recently observed inflation
Rational expectations: People form their expectations based on all available information, including information about current and prospective future policies.
Example: If BoC announces shift in inflation target, if expectations are adaptive, then expected inflation will not change because it is based on past inflation. If expectations are rational, expected inflation will change because people will factor the announcement into their forecast.
Adaptive expectations
EΟ = Ο-1
Ο-1 = last year's inflation
Inflation inertia: In this form (Ο = Ο-1 - π(u - un) + π)
In the absence of supply shocks or cyclical unemployment, inflation will continue indefinitely at this rate
Past inflation influences expected current inflation, which influences wages and prices that people set.
Phillips curve becomes:
Ο = Ο-1 - π(u - un) + π
In this case, natural rate on employment called NAIRU: Non-Accelerating Inflation Rate of Unemployment
Two causes of rising and falling inflation
Cost push inflation: inflation resulting from supply shocks
Demand pull inflation: Inflation resulting from demand shocks
Favourable supply shock pushes cost down, decreasing inflation.
Adverse supply shock raises cost of input, pushing prices/ inflation up.
Positive shocks to aggregate demand causes unemployment to fall, pulling inflation rate up
Negative demand shock raises cyclical unemployment, brings inflation down
Affects EΟ + π
Affects -π(u - un)
Painless disinflation
Proponents of rational expectations believe that sacrifice ration my be very small. If BoC announces it will reduces inflation, and BoC announcement is credible, EΟ may fall, causing Ο to fall, without any need to change u, and causing unemployment to stay at natural rate u = un
Central banks that are politically independent are more credible than those with political ties. Therefore it is less costly for central banks to reduce inflation if they are independent.