QUESTION 2 (14 points)

Consider the following cobweb model of labor market: $L_{t}^{s} = - 10 + 0.9 W_{t - 1}$ , and $L_{t}^{d} = 100 - 0.6 W_{t}$

Answer

For general model, $- 10 + 0.9 W_{t - 1} = 100 - 0.6 W_{t}$ , $W_{t} = \frac{1000 - 9 W _{t - 1}}{6} = \frac{550}{3} - \frac{3}{2} W_{t - 1}$ , so $a = \frac{550}{3}$ , $b = \frac{3}{2}$ .
Since we don’t know $W_{0}$ , $y_{t} = [y_{0} - \frac{a}{1 - b}] b^{t} + \frac{a}{1 - b}$ is the LR wage rate (General Equation)

$W_{t} = [W_{0} - \frac{220}{3}] (- 1.5)^{t} + \frac{220}{3}$ , so $∣ b ∣ > 1$ , it is unstable.

From the given, $W^{*} = 73.3$ , in the model, we assume $W_{0} = 75$ .