Applied Consumption Analysis by L. Phlips
By L. Phlips
This quantity hyperlinks the summary idea of call for with its econometric implementation. workouts lead the reader from straight forward application maximization to the main refined contemporary suggestions, highlighting the most steps within the historic evolution of the topic.
The first half provides a short dialogue of duality and versatile varieties, and specifically of Deaton and Muellbauers ``almost excellent call for method. half comprises the authors paintings on actual salary indexes, and on intertemporal software maximization.
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2 (d) Impose d u/dxf = au < 0. (e) I find the system ö Xi = Xl = 2 011 - 01 + 022 0 1 - 0 2 111 + 022 22 . «Il , + + a 022 011 J 011 + 022 Adding up these two linear Engel curves, I find that the two intercepts sum to zero (the first is the negative of the second) and that the slopes sum to one. Why should this be? It is worth noting that the early marginalist writers worked with additive utility functions. Because of the impact of ordinalism, these functions disappeared from the scene for many years (to reappear in the sixties, only, with the development of applied econometric work in the field).
B) Verify that ku < 0 and kX2 = k2l. (c) Explain why pf is the only price that appears in the demand equation for good /. Answer: (a) Total differentiation of the first order conditions x2 - Λ Ρ Ι = 0 x, - λρ2 = 0 χ y - Ρ\ \ χ = ο - Ρι 2 gives — Pi d/ = / άρχ — ρ2άλ = λ dp2 dx2 = - d y + xl dpx + x 2 dp 2 d*2 dxx — ρχ dxx — ρ2 so that 0 1 D 1 0 •Pi -Pi o n = -Pi dxx = "Pi - p 2 = 2p,p 2 0 Du = PiPi D31 = - p 2. — P&dpx 4- P i P 2 ^ d p 2 - p 2 ( - d y + x, dpx + x 2 dp2) 2PiPi and for dp 2 = dy = 0 dxx and ρ2λ χ, 2Ρι 2Pi Demand functions: general restrictions 46 (b) A, px and p2 being positive, kx What about /c 2 2?
A few standard tricks are presented in the following exercises. 4. The double-logarithmic specification *i = M n n"y\ xl l2 in which good 1 is the particular commodity to be analysed, and goods 2 and 3 are close substitutes or complements, is very popular. How would you impose the homogeneity restriction? Answer: The restriction is fill + / » 1 2 + 0 1 3 + y = O. 38 Demand functions: general restrictions It is sufficient to make sure that y = — ßw — ß\2 ~ ßu- This is obtained by writing the demand equation as ^J"^J ^J I2 χχ = ΑρΙ"ρΙ»ρξ»γ-'»-'»-'» = A 13 and to run the multiple regression l o g x !