Macroeconomics Week 4: Short-Run Aggregate Supply and the Phillips Curve

Question 1

Describe & interpret the simple representation of the short-run supply model

What’s the issue with it? What can we do about it?

Answer 1

• “Income, output, Y” as x-axis and “Price level, P” at y-axis.
• Horizontal line, “SRAS” drawn from y-axis
• Vertical line, “LRAS” drawn from x-axis, where there’s a point “Ybar”.
• Point “A” is where LRAS and SRAS cross. There’s also a downard (with a positive d^2 y / dx^2) sloping line, “ADbottom right1”.
• There’s another slope parallel to AD1, on its right, “AD2”.
• Arrow from AD1 to AD2 (representing a shift in AD), with label “1. A rise in aggregate demand…”
• Point “B” at where AD2 and SRAS cross with label “2. …raises output in the short run…”. Also, arrows going through SRAS from A to B.
• Point “C” at where AD2 and LRAS cross with label “3. …but in the long run only affects the price level.”. Also, arrows going through AD2 from B to C.

Interpretation

Key point: shifts in AD only affect output in the short-
run and only affect the price level in the long-run.
It’s as if prices cannot change in the short-run. This is
not particularly realistic, with the possible exception of
a deep recession/depression (Keynes).
Now: we still accept that shocks/policy changes affect
only the price level in the long-run (A to C) but we need
to rethink the short-run (A to B).
We can generalise the short-run relationship to an
intermediate case in which the SRAS curve is upward
sloping (‘new Keynesian’ approach) and use this new SRAS to derive the ‘Phillips curve’.

Question 2

What can we derive from the ‘new’ SRAS model?

Answer 2

The Phillips Curve

Question 3

What does the Phillips Curve show?

Answer 3

• The Phillips curve shows the short-run tradeoff
  between inflation and unemployment…
  …but the tradeoff is temporary (it only applies in the
  short-run); this has important policy implications.

Question 4

Briefly describe the 2 difference aspects that are considered when modelling the short-run tradeoff illustrated by the Phllips Curve

Answer 4

How do we model this temporary tradeoff?
- We shall consider two different types:
1. Sticky prices: some fraction of prices are fixed and
the remainder are flexible (Keynes did introduce frictions, as shown by how prices don’t change in the short term, but it’s very extreme. For context, Keynes came up with the model when the Great Depression occurred and models at the time could not explain what was happening. But over the last few years, it’s apparent that Keynes’ model is not totally correct - prices do change in recessions and stuff. The new SRAS curve sorts this out).
2. Imperfect information: the general price level is not perfectly observed.
- Each offers a different explanation. Either way, we arrive
at the same equation for the SRAS

Question 5

Describe the equation that we arrive at for SRAS to help derive the 2 models for the Phillips Curve

How can we rearrange this?

Answer 5

Y = Ybar + alpha(P-EP) (1)

where
Y = output, Ybar = ‘Natural level of output’, parameter alpha > 0, P = General price level and EP = Expected general price level
- Output differs from its ‘natural level’ if P does not equal EP
- Almost all decisions have a forward-looking variable, so does this model
- Rearrange (1) In Terms of P:

P = EP + 1/alpha x (Y-Ybar) (2)

where 1/α (>0) is the slope of the SRAS when
plotted with P on the y-axis and Y on the x-axis (because alpha is positive, naturally, 1/alpha is positive. Hence, upwards sloping curve)

Question 6

Describe & explain the ‘sticky price’ model for the Phillips Curve

Answer 6

• To understand this relationship between inflation and unemployment, consider each
  model in turn; they offer different explanations.
• Economists debate the importance of sticky prices, that’s why there are 2 models. Both will be shown to cover all bases:

Model 1: The Sticky-Price Model

Widely used in Macro models (e.g. by central banks).
Key friction: firms do not immediately adjust their
prices following a change in demand for their
product/service.
Why not?
– Long-term agreements with customers
– ‘Menu costs’ - When there’s a tiny increase in demand so technically prices should rise by a tiny amount; but money has already been spent to set the price at what it was (like to print menus), so it’s not economically viable to do it
– Sticky wages (labour is an important FofP)

p = P+alpha(Y-Ybar)
where alpha>0 and p = An Individual Firm’s ‘Desired’ Price

• The firm’s costs
  are higher when P
  is higher (e.g.
  nominal wages)
• A higher level of
  aggregate income
  (GDP = Y) raises demand
  for the firm’s product
• Firms would set the price p if they were able to adjust continuously. So this would be the equation for flexible prices, where firms always set prices as desired
  Firms with sticky prices must set price in advance:
  𝑝 = 𝐸𝑃 + 𝑎(𝐸𝑌 − 𝐸𝑌bar)
  Further assume that 𝐸𝑌 = 𝐸𝑌bar, then 𝑝 = 𝐸𝑃 for the sticky price firms.

Denote the fraction of firms with sticky prices as ‘s’
(where 0 < s < 1):
P = sEP + (1-s)[P+alpha(Y-YBar)]
‘sEP’ is for those firms with sticky prices and the rest if for flexible prices firms.
This is simply a weighted average of the prices set
by the two groups of firms.

Rearrange To Give:
𝑃 = 𝐸𝑃 + ((1 − 𝑠)/s) x 𝑎(𝑌 − 𝑌bar)
And compare this to P = EP + 1/alpha x (Y-Ybar) Implies that:
1/𝛼 = (1 − 𝑠)/𝑠, 𝑎 > 0
Interpretation in this model…