武漢大學(xué)mba管理經(jīng)濟(jì)學(xué)第三章-資料下載頁
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【正文】 ect to an ine constraint: I = Px?X + Py?Y ? Graph in 3dimensions Y X U Uo Uo Slide 26 Consumer Choice assume consumers can rank preferences, that more is better than less (nonsatiation), that preferences are transitive, and that individuals have diminishing marginal rates of substitution. Then indifference curves slope down, never intersect, and are convex to the origin. X Y 5 6 7 9 7 6 convex Uo U1 U2 give up 2X for a Y Slide 27 X Y Y Uo U1 a c demand b Indifference Curves ? We can derive a demand curve graphically from maximization of utility subject to a budget constraint. As price falls, we tend to buy more due to (i) the Ine Effect and (ii) the Substitution Effect. Py Slide 28 Consumer Choice amp。 Lagrangians ? The consumer choice problem can be made into a Lagrangian ? Max L = U(X, Y) ??{Px?X + Py?Y I } i) ?L / ?X = ?U/?X ? Px = 0 MUx = Px ii) ?L / ?Y = ?U/?Y ? Py = 0 MUy = Py iii) Px?X + Py?Y I = 0 ? Equations i) and ii) are rearranged on the righthandside after the bracket to show that the ratio of MU’s equals the ratio of prices. This is the equimarginal principle for optimal consumption } Slide 29 Optimal Consumption Point ? Rearranging we get the Decision Rule: ? MUx / Px = MUy / Py = MUz / Pz “the marginal utility per dollar in each use is equal” ? Lambda is the marginal utility of money Suppose MU1 = 20, and MU2 = 50 and P1 = 5, and P2 = 25 are you maximizing utility? Slide 30 Problem ? Max L = 2X + 2Y +XY .6Y2 ? {48 4X 6Y } 1. Lx: 2 X + Y = 4 ? 2. Ly: 2 + X = 6 ? 3. L?: 48 4X 6Y = 0 (1) and (2) yields: X = ?Y + .4 (3) can be reduced to X = 12 Together we get: X = , Y = Substitute X and Y into (1) we find ? = .31 X = ?Y + .4
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