Question

Consider the following economy of exchange. There are two goods and two consumers. The two goods...

Consider the following economy of exchange. There are two goods and two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2.

Consumer 1 has the utility function U1(t, q) = . 4ln(t)+ . 6ln(q) (where t is the amount of tillip and q is the amount of quillip).

Consumer 2 has the utility function U2(t,q)=. 5ln(t)+. 5ln(q).

Consumer 1 is equipped with 10units of quillip and tillip each. Consumer 2 is equipped with 10 quillip units and 5 tillip units.

a) What is the Walrasian equilibrium of this economy? ( If there is more than one equilibrium write them all down).

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Answer #1

Ui(tiq)- 0-4 ln t +0.6 ln q entot + engub Since stility ultiq = 0.4 0.6 - en t q is an ordinal concept t t et qui oo Similary2 2 2 2 2 =P 29= 3t p q= ЗЕР Substituting in Income constraint Pt+lq < 10 p +10 3pt 10C1+p) pt tapt 5 pt = 10(1+p) 2 t = to CU₂ (t,q)= to 5 Consumer 2 0.5 max to 5quos Sub.to pt tlq = 1045p - MUE Р Muq aulot subg P 오 I 7) t q=pt Substitute in incomeTotal demand of quilep- Total endowment of quelp 10+52 + 6(1+p) = 20 2 5+2.5p +6+ 6p = 20 11 +8.5p = 20 8.5 p=9 p=9 8-5 P. 16

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