Question

The utility function is u = 3x1 + x2, and the budget constraint is m = p1x1 + p2x2.

a) What are the demand functions x1(m,p1,p2) and x1(m,p1,p2)? For m=100, p1=4 and p2=1, what are the consumption amounts x1 and x2?

b) Assume only p1 changes to p1’=2, define the new consumption values as x1M and x2M.

c) Define as uH the utility amount you get from consumption bundle in part a. Find the consumption bundle (x1H,x2H) that gives you the same utility (uH = 3x1 + x2), but that satisfies the new budget line slope p1’/p2 with the new prices (p1’=2 instead of p1=4).

d) Compare x1M from part b and x1H from part c. Do they differ? What is the substitution effect and the income effect of this price change?

Answer 1

Since is the utility function U= 3x + x2 we know it is Condition a perfect substitute. given m= Pix, + P2 X₂ P = 4 P = 1 Line P>P2 : 471 a rationale consumer will all of ₂ and none of choose a X2 = m i.e 100 = loo ni = 0 n (m, Pype) = 0 x cm., pp.) = 100 The is consumption (0, 100) for m=100, P,= 4 and peel

ch - Now instead of 4. since Pi>P₂ ginen same, pia ; 271 m = 100 is seill the the consumer X2 and will none all consume of a of 100 - 100 21 O So, the is new consumption bundle (12,5", 23") = (0,100) 2 from past (a) (1,4, x, h) = (0,100); u 300 h UW 3 (0) + 100 U"=100 The various consumption bundles that satisfies. the above utility and new prices area is; U-20 tku m = Pín, & P.. weith Pix 2 , p. 1 MRS =P P

a comparing xim and why we conclude that they do not differ but unstead remains the same. With change in price of xi from 4 to 2 our purchasing power increased because now the same x can be obtained at low puce but we still choose Us over no this is because x is still cheaper than n, and they being substitutes beople still prefer to by X2 . Here substitution effect over powers income effect.