Lent - Lecture 8 - Short-run Aggregate Supply

Question 1

The AS curve slope upwards in (π, Y) space in the short run, of what form? (what is the AS equation?)

Answer 1

π = π(e) + v(Y - Y̅) + ε

Question 2

What are the 3 stories/justifications for the SRAS curve?

Answer 2

• sticky prices
• sticky wages
• imperfect information

Question 3

Describe the story for sticky prices producing an AS curve, getting to the point: π = π(e) + v(Y - Y̅)

Answer 3

• suppose a fixed share of firms s have fixed prices, in advance of current period, whereas (1 − s) firms are free to vary
• aggregate price given by P:
• P = s(ps) + (1 - s)(pf), ps - sticky prices, pf - flexible prices
• firms assumed to want to set prices as function of P and (Y - Y̅): p = P + a(Y - Y̅)
• higher P ⇒ set own price higher in response to other, higher (Y - Y̅) ⇒ higher marginal costs (real wage, inputs…)
• (think of p, P as log prices)
• for flexible firms, pf = p, for sticky firms, ps = p(e)
• assume sticky-price firms expect Y = Y̅, hence ps = P(e)
• aggregate price level then satisfies:
• P = sP(e) + (1 - s)[P + a(Y - Y̅)]
• P = P(e) + (a(1 - s)/s)(Y - Y̅)
• to get to (π, Y ) space subtract P(-1) from both sides, P(-1): : last period’s (log) aggregate price level
• P - P(-1) = P(e) - P(-1) + (a(1 - s)/s)(Y - Y̅)
• π = π(e) + v(Y - Y̅), where v = a(1 - s)/s

Question 4

Describe the story for sticky wages producing an AS curve, getting to the point: π = π(e) + v(Y - Y̅)

Answer 4

• workers and firms bargain over wage rate in advance and agree on fixed nominal value:
• W = ωP(e); W: nominal wage; ω: target real wage
• the actual real wage:
• W/P = ωP(e) / P
• think of a Cobb-Douglas production function where K is fixed in the SR, labour is hired until real wage equals MPL (Y = A(K^α)(L^(1-α)))
• this can be re-arranged to solve for employment as a function of prices
• a higher price level drives down the real wage, increasing employment, causing output to rise
• if Y̅ is output when P = P(e), use algebra to show: Y = Y̅ (P / P(e))^((1 - α)/α)
• rewriting as logs would give: Y = Y̅ + ((1 - α)/α) (P - P(e))
• re-arranging and subtracting P(-1) from both sides, P(-1): : last period’s (log) aggregate price level, gives:
• π = π(e) + v(Y - Y̅), where v = α / (1 - α)

Question 5

Describe the story for imperfect information producing an AS curve, getting to the point: π = π(e) + v(Y - Y̅)

Answer 5

• the economy consists of a large archipelago
• each island in the archipelago produces a different product
• there are many producers on each island
• every month the local Walrasian auctioneer rows to each island and announces the nominal price of its good, p
• the islanders then decide how much to produce at this price, y
• higher y raises real marginal cost, MC (y )
• if they knew the real price of their goods, perfect competition would ensure: p/P = MC(y)
• the islanders are rational, and have formed expectations about the price their product should sell for, p(e) , and their output, y(e)
• when they see p > p(e), the islanders ask themselves:
• has the rest of the archipelago finally recognised the superiority of our product? ⇒ p/P ↑
• or has the value of money just fallen everywhere? ⇒ P↑, p/P constant
• key point is that with some probability, either of these could be true! ⇒ nominal price is an imperfect signal of real demand
• if it is that relative pries have risen, we will have p/P > MC unless y rises above y(e)
• if it is that general price level has risen, we will want to keep production constant
• provided there is some probability on a relative price rise, each island sets y higher when p is higher: y = y(e) + α(p - p(e))
• this aggregates up to give AS: Y = Y̅ + α(P - P(e)), Y̅: output when real prices perfectly known (Classical case)
• can rearrange, subtracting P(-1) from both sides, etc, to form: π = π(e) + v(Y - Y̅)

Question 6

Give 1 criticism of each approach to derive the SRAS curve

Answer 6

• why are workers wiling to move off their labour supply curves? (sticky wages)
• why are sticky-price firms willing to produce where MR < MC?
• what happens when the islanders get internet/broadband, is there imperfect information nowadays?