Question

Question 1: Robert and Erin are trapped on a deserted island with only two goods: Wine (W) and Crackers (C). Robert currently has 6 bottles of wine and 9 boxes crackers whereas Erin has 9 bottles of wine and 6 boxes of crackers. Robert's preferences are represented by his utility function UR = W0.6C0.4 and Erin's by UE = W0.400.6.

Answer 1

(d) Budget constoint where bw=price W. pwr C. pc =m of wine Pc = Price 1 W. pw + cop c = 6 b. wt q pol Robert of Crackers Exin's Wo kw + c. pe =m w.pw tc pc = 9 Pw to pc Note these Two's can be further Simplified.

and litiit 0.6 0.6 endowment of Robert's (6,9) and Utility UR = wº coccy & crackers . (el equilibruim Conclition. MRS = Pc Juldw - PW Jolte bo -0.4 0.4 Oo6 wc bw - 0.6 -0.6 - 0.4 m с 0.4 0.6 Goic - bw 0.6 ay Wow =) 1056= w Budget construint equation pw. wt pc. c = m. kw. wt bc. c = 6 pw + 9 kc toom Pw 1 P =) kw=pe bco(1.50) + bc. c = 6 pct a b c

Pc (1.5c) + PooC = 15 pc 2.5c pc = 15 kc =) 2.56 = 15 po pc =) 2.5 c = 15 - c = 15 25 C = 6 there Jove w = 6. (105) w=9 Now for Esin's enclowment (9,6) equilibruim Concution MRS = bw PC -0.6 0.6 c 0.4 w 0.4 -004 0.6 Wic 0-6 0.4 4 cc 6 wou woo - - - = 1 =) als 0/3

46= 66 - C = 60 from Pw = 1 => c= 1.56 Budget construint equation kw. W + bc. c=m kwow tPc. (1.5w) = quart 9 put bbc =) bw = pc Pwowa pw. 1.5w = q pwr 6 kw 2.5w pw = 15 pw =) = 15 259 = 6 =) there Jore, C= 1.5(W) = 105 (6) = 9. XR - (9,6), endowmento = (6.9) [LXE = (6.9), endowment E= (96) Demand Functions.

Robert's demand of wine is a bottles and it has endlow ment of 6 Bottles So he want to buy 3 Bottles of wine. Erinls demand of wine is 6 bottles and it has endowment of 9 Bottles, So he want to sell 3 Bottle -wine. Total Supply of Born goods are (15,15 ) = (exter, eater) (679, 956) - (15,15 )

Budget line good c is 2 - - - - - - - - - 2 |-- -|- - - - N c quilibouim - - - - - - - - - - - 1 2 3 4 5 6 7 8 9 10 11 12 13 good wts 0 Robert OR equilibrium = fincel allocation.