The Cobweb Model

17.21. For the data given below, determine (a) the market pricc P, in any time period, (b) the equilibrium price P„ and (c) the stability of the time path.

u) Equating demand and supply.

Dividing through by -0.75 and using (17.4).

/>,- -0.4/%, + 280- (220-y^j(-0.4)' + Y^-20(-0.4)' + 200 (J7.23)

/>) If the market is in equilibrium. P, = P, ,. Substituting P, lor P, and P,.x in (¡7.22).

which is the second term on the right-hand side of (1733). c) With b - -0 4. the time path P, will oscillate and converge.

17.22. Check the answer to Problem 1721(«). using t = 0 and i - 1.

From (17.23), P0 - 20(-0.4)° + 200 - 220 and P, 20( -0.4) +■ 200 - 102. Substituting P, for /', and P„ for P, , in (17.22).

17.23. Redo Problem 17.21. given Q+ = 160 -0.8/V Q„ = -20 + 0.4P,.,. and P0 * 153.

Dividing through by -0.8 and using (17.4).

b) As shown in Problem l?.2l(fc). P, - 150. See also Section 17 5. r) With b = -0,5. P, oscillates and converges toward 150.

17.24. Check ihe answer lo Problem 17.23(a), using / 0 and t = 1.

From (17.25). P„ - 3(~0.5)" + 150 - 153 and P, - 3(-a5) + 150 - 148.5. Substituting in (17.24).

17.25. Redo Problem 17.21. given = 220 - 0.4P,. Q„ = -30 + 0.6/»,.,. and P0 = 254.

Dividing through by -0.4 and then using (17.4).

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