Question

Use the sticky-wage theory of aggregate supply to explain the short-run Phillips Curve

Answer 1

We first derive the aggregate supply equation using Sticky-Wage Theory:

Nominal Wage (W) is set on basis of target w and Price level Pe
W = w*Pe
Dividing both sides by P
W/P = w*(Pe/P)

w = target real wage

Three possibilities:
If P = Pe, then output is at natural level
If P > Pe, then ?rms higher more workers and output will rise above the natural level
If P < Pe, then output is less than the natural level
Now, a typical ?rm will set the desired price level as following:

p = P + (Y - Ybar)

> 0

Y bar is the natural level of output
In the sticky price model, firms must set an expectation of price and output level. So,
p = Pe + (Ye - Ybar)

Now let f = fraction of firms with sticky prices , then above equation can be written as:
P = sPe + (1 - s)[P + (Y - Ybar)]

where Pe = price set by sticky price firms
and P + (Y - Ybar) set by the flexible price firms
Now, we subtract (1-s)P from both LHS and RHS

sP = sPe + (1-s)[ (Y - Ybar)]
Divide both sides by s

P = Pe + [(1-s) /s]*(Y - Ybar)
Now, solving for Y

[(1-s) /s]*(Y - Ybar) = P - Pe

(Y - Ybar) = [s /(1-s) ] * (P - Pe)

Y = Ybar + * (P - Pe) : AS equation

Short Run Phillips Curve:

= e -  *(U - Un) +

where = actual inflation rate

e= Expected inflation rate

U - Un = Cyclical Unemployment

= measure of supply shock

measures the response inflation to cyclical unemployment

AS curve shows how Output is related to unexpected changes in the price level

Phillips curve shows unemployment is related to unexpected changes in inflation rate. The curve is the reflection of the aggregate supply curve. When there is movement along the supply curve, unemployment and inflation changes in opposite direction

**if you liked the answer, then please upvote. Would be motivating for me. Thanks.