Answers
ucan, an) = q + 10 log 92 and m.
P. and P2 Ane (1) fog marshallion Demand functions, 9, and we max u= 9, + 10 log Q2 Sit m= br. 9, + P2 • Q2 Setting Lagrongian. 2 = 9,1 + 10 logar + d [ P.2, + kr 92-m] - It db = 0 =) db = -1 IL d91- - da 1-0 - + dbz -0 => 1 - 10 tij 92. P2 Comparing (il ancel (in - - 10 Bi qe pe - Q2.
P2 = -10p, =) loki = q. 2.kz
Now P,.qit bioait p2-92 = topi = m. m. prl Prod = m- lopi a = m-lopi = m-lopi - Pipi from lopi = 92. P2 - Q2 = lopi P2.
Q = m-lopi q2 = lopi 21 p2 Ans-2 Indirect utility function. ucan, O2) = 9, + 10 loga, -m-1061 + 10.10g (lon) PI - 10 + lo log ( - 0 (+ log (oh)) urai, au)
Ans-3 Hicksian demand functions max. m= P, .91+ P2-92 st u= 9, + 10 log2 L = p.ait pr. q2t, pi- = 0 = = pi. 391 the = P2 - 1 10 20 ) 2 = 1 1 0 >> br.v2 - (ii 10 comferning (is ana (i bi= b 2 +92 10 lopi = P2 & Q2 = Q = loki bz r e spot using this in constraint Function u=9, + 10 log 2 - 9 + 10 llopi , (P2)
U = q + 100 bi p2 - =q, U - 100 PI p2 - Ub-loobi =q, where as Q2 = lobi p2 So ricksian demand 9 = functions UP2-loopi = U-loopi p2 q2.
.
Lobi pz (iv) Expenditure function. m(BI, 62, 0) = p. h(b. cul = b.q, (0, p.) + Pr. 92 (0, P2) = pi (0-100 ky ) + pr.
Lopu m(b, es, u) = bilu- loop," It lopi p2 J
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