Question

Suppose that instead of having a fixed income I, you have an endowment of y = 12 units of You can sell each of these units of good Y at price Pj and use the proceeds to buy good X, which good Y has a price of P Draw your budget line if P = 3 andP, = 4 Draw what happens to your budget line if P increases from 3 to 4, or if P, decreases from 4 to 3. How is this different from the effect of price changes if you had a fixed dollar income? Suppose you have the simple Cobb-Douglas utility function u(x, y) = xy. Solve for your optimal consumption (x*, y*) as a function of the exogenous variables y, Pr, and Py

Answer 1

Find solution in the pictures attached below

Guiuun, yE= 12units S, 4our imcomu 12-2 M: a) P3 and 4- ヤ·てこし ぐ 48 purchau con So, Manimum amount ct xau M 3 = 48 -interapt) 16 Manimum amount o Y yau purhaue can M 4 48 12 units. 4-imter cap) 20 16 4 16 20 24 1 2 4 sla

(b) Pr 4 Py 3 thon -12 x3 - 36 Maximum amaunt c puchau, M' 36 4 9 C2-inteuupt) Pa Marimum ameunt punchaie M' 36 12 Ly-interupt)

15 3 9 12 IS

Now when ue Campuru u th that inter cept has decreaied fart 'a Obser we uue but -intercapt has guemainad tha sume That the budget line has rotated 12 (Rotation of budget Line) 3 7 x 3 15 18 12 duppose that the M= $ 48- 的7hen uulth Pu-4 income was But fired ay and Py wiu change ous -intercapt anel y-inteupt both 3 ,i e 48 2-interupt - 12 d intecapt4 16 wiu be hipt ef budget there This means Line 12 16 20 12

(c) utility Jubject You objectua is to manimise to constraint, M Lag range Sel up +he Ore First ordu candihons and a So, Le8 y : Yr- R A PM *i And 2-ARy APY Diuide O by A PR 2 2

budget Constrainl, Substitut in Py h.%dR. R.34 By Symmetry can upute , PM tenu optimal consumphion bundle ¥) 2

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