Question

Suppose Bob consumes two goods *; and *a. His budget is $20 and the market prices of *1 and ta are P1 = 2 and Pa = 2 respectively. The utility of Bob of consuming $1 units of X1 and 42 units of Iz is u (31. 12) = V7+2 Vs Suppose that the price Pa drops from $2 to $1. The subsitution effect of the price change of P. is a. Bob consumes more * and consumes the same amount of my OD. Bob buys 4 units more of 1 and 2 units less of tz O Bob buys 2 units more of 1 and 2 units less of a Od Bob buys 5 units more of X, and į units less of X3 14

Answer 1

THE STEP BY STEP SOLUTION IS AS FOLLOWS-

Given & - () = {ч + 2 x, 2. 12² Z2 Ya 2.0 M 0x1 = 1 МОх, ? 2 Гя, 2 งาน а. 2. L, 2. MRS = Muay Mх, P, P2 р P? ЧЧ 21- Оy P, 2 та 4 mpi чер че? budget >> constraint = P = up, + xz pz үс чрағp(чтары) PhXzp>) + Mz pe ( че ү. чр, + 44р. жар Чет Үра - 4 ( Pop, +4р. ) Че, Yama (p, +4 РР.) *, ура Чр, У Рів. + Че: pot 4 popa 2 Y у X Р: Р С. 4 - 20х2 2. и,- Чx2 х 20 BE ИНАЧ Ч+ЧxЧ . mm 1. f Y = xipit na і Ръ 2x | +8х2 = 10 =

4 2 Y' 18 2 १ 4116-6 2 2+4 418 Substitution effect o> for no = 2' - , - 6-2 4 tov x2 : 1,' - , - 6-8- -2 tor 273 1/3 म - 2 S S 24 P:5_y- 20 f MU x = du d dxi ।/3 2 22 13 MUna ed U - dra 2/3 A 2/3 34 3 243 1/2 42 2 ८१८ MRS = Muxi M Uxz 302 2/3 113 24 - 24 P2 3 . he In OY 42 2 - 232P2 4. pi 22 Burlget constraint, r=upi tu, pe १- F/23) NP Y: 4 + PAP + fI edene Ek 21 - 3 34 20 - 1 2X20 - X* - Y 3 2* - 21 3 3X5 3 3 2x3 14 20 4 3 3

GENRALLY WE FOUND THE MRS USING DIFFERENTIATION OF U AND THEN WE FOUND A RELATION BETWEEN X1 X2

AND THEN WE USED THEM AND BUDGET CONSTRAINT TO FOUND X1* AND X2* THEN WE INSERTED THE VALUES GIVEN AND FOUND OUR REQUIRED VALUES.

FOR FIRST WE FOUND NEW INCOME FOR NEW PRICES AND NEW X1' X2'

ANSWERS-

FOR 1- B) BOB BUYS 4UNIT MORE OF X1 AND 2 UNIT LESS OF X2

FOR 2-B) 20/3,4/3

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