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Question 2 Carol has the following utility function: Uc = (xc)0.6 (4c)0.4 where xc and yc are the quantities of x and y consu(b) Derive Carols demand equations for x and y using this Lagrangian. (6)The only other person in this economy is Alex who has endowments TA = 80 and YA = 40. The aggregate demands for x and y in th(d) Given Carol and Alexs endowments and assuming Py = 1, find px and the relative price (2) for a competitive general equil

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e Giren utility function of carol: we = ( x ) = (y jou Carols budget constraint: 100 (Py + Py) = P xe + py =100 and rc = 100W Now, from (3) and and (4) ► 100 (P + Py) - 32 Py. Ye - Py. Ye = 0 or, 100 (Pet Py) - 5 Py. Ye =0. on 100 (P2 + Py) = 5 Py.At equilibrium heative price - Prati or. Por at Los Carols Demand: Ye = 40 Pet Py. x = 6o Pat Py. Pg or xe = 60 t tt 2 40 ItYA 2 Y - Ye = 80 px + 60Pg. 90 (Pet Py) (80 - 40) Pa + (60-40) Py. 40 Pa + 20 Pg. 2 (40+2) + (20+4) carol: consumed Hmol quan

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