Economics Dynamics Problems 155

# Economics Dynamics Problems 155 - Discrete dynamic systems...

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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, Y 0 = 20, and b = 0 . 8 and 1.2, respectively. For what period does the system converge on Y Y 0 within 1% deviation from equilibrium? For the same initial value Y 0 , is the period longer or shorter in approaching equilibrium the higher the value of
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