11.9 Cobweb models One way to generate disequilibrium prices in a simple model of supply and demand is to incorporate a lag into producer’s supply response. To examine this possibility, assume that quantity demanded in period t depends on price in that period (Q D

t = a − bPt

)

but that quantity supplied depends on the previous period’s price – perhaps because farmers refer to that price in planting a crop (Q S

t = c + dPt−1).

a.

What is the equilibrium price in this model (P* =

Pt = Pt – 1) for all periods, t ?

b.

c.

d.

e.

f.

If P0 represents an initial price for this good to which suppliers respond, what will the value of P1 be?

By repeated substitution, develop a formula for any arbitrary Pt as a function of P0 and t.

Use your results from part

(a) to restate the value of Pt as a function of P0, P* and t.

Under what conditions will Pt converge to P*

as t → ∞?

Graph your results for the case a = 4, b = 2, c =

1, d = 1 and P0 = 0. Use your graph to discuss the origin of the term cobweb model.