tailieunhanh - Basic Mathematics for Economists phần 9

Thuê xe tổng hóa đơn cho mỗi tuần sau đó có thể được tính bằng cách nhân số lượng xe ô tô trong mỗi thể loại được thuê với giá tương ứng. Ma trận được định nghĩa như là một mảng của các số (hoặc ký hiệu đại số) đặt ra trong các hàng và cột. | Now substitute this value for P0 into the general solution 2 above so that P0 55 45 A -1 0 55 45 A 10 A The specific solution to the difference equation for this example is therefore Pt 45 10 -1 Using this formula to calculate the first few values of Pt we see that P0 45 10 -1 0 45 10 55 P1 45 10 -1 1 45 - 10 35 P2 45 10 -1 2 45 10 55 P3 45 10 -1 3 45 - 10 35 P4 45 10 -1 4 45 10 55 etc. Price therefore continually fluctuates between 35 and 55. This is the third possibility in the stability conditions examined earlier. In this example d b 2 -2 - 1 1 Therefore as t TO Pt neither converges on its equilibrium level nor explodes until the market collapses. This fluctuation between two price levels from year to year is sometimes observed in certain agricultural markets. Test Yourself Exercise Assume that the usual cobweb assumptions apply in these questions. 1. In a market where Qd 160 - 20Pt and Qt -80 40Pt-1 quantity unexpectedly drops from its equilibrium value to 75. Derive the difference equation which will calculate price in the time periods following this event. 2. If Qd 180 - and Qs -24 say whether or not the long-run equilibrium price is stable and then use the difference equation method to calculate price in the thirtieth time period after a sudden one-off increase in quantity to 117. 1993 2003 Mike Rosser 3. Given the demand and supply schedules Qd 3450 - 6Pt and Qs -729 Pt-1 use difference equations to predict what price will be in the tenth time period after an unexpected drop in quantity to 354 assuming that the market was previously in long-run equilibrium. The lagged Keynesian macroeconomic model In the basic Keynesian model of the determination of national income if foreign trade and government taxation and expenditure are excluded the model reduces to the accounting identity Y C I 1 and the consumption function C a bY 2 To determine the equilibrium level of national income Y we substitute 2 into 1 giving Y a bY I Y 1 - b a I