Discrete dynamic systems 139 7. Derive the cobweb system for the price in each of the following de-mand and supply systems, and establish whether the equilibrium price is (i) stable, (ii) unstable, or (iii) oscillatory. (i) q d t = 10 − 3 p t q s t = 2 + p t − 1 q d t = q s t (ii) q d t = 25 − 4 p t q s t = 3 + 4 p t − 1 q d t = q s t (iii) q d t = 45 − 2 . 5 p t q s t = 5 + 7 . 5 p t − 1 q d t = q s t 8. Suppose we have the macroeconomic model C t = a + bY t − 1 E t = C t + I t + G t Y t = E t where C and Y are endogenous and I and G are exogenous. Derive the gen-eral solution for Y n . Under what conditions is the equilibrium of income, Y ∗ , stable? 9. Verify your results of question 8 by using a spreadsheet and letting I = 10, G = 20, a = 50, Y0 = 20, and b =0 . 8 and 1.2, respectively. For what period does the system converge on Y ∗ − Y0 within 1% deviation from equilibrium? For the same initial value Y0 , is the period longer or shorter in approaching equilibrium the higher the value of
This is the end of the preview.
access the rest of the document.