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 1QD t 5 a 2 bPt 2 but that quantity supplied depends 17The seventeenth-century French finance minister Jean-Baptiste Colbert captured the essence of the problem with his memorable statement that “the art of taxation consists in so plucking the goose as to obtain the largest possible amount of feathers with the smallest amount of hissing.”

18See F. Ramsey, “A Contribution to the Theory of Taxation,” Economic Journal

(March 1927): 47–61.

on the previous period’s price—perhaps because farmers refer to that price in planting a crop 1QS t 5 c 1 dPt212.

a. What is the equilibrium price in this model 1P∗ 5 Pt 5 Pt212 for all periods, t.

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

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

d. Use your results from part

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

e. Under what conditions will Pt converge to P∗ as t S q?

f. Graph your results for the case a 5 4, b 5 2, c 5 1, d 5 1, and P0 5 0. Use your graph to discuss the origin of the term cobweb model.