Consider a pure-exchange economy, with two consumers and two commodities. Initial endowments are given by w1...

Consider a pure-exchange economy, with two consumers and two commodities. Initial endowments are given by w1 = (4, 2) and w2 = (2, 3). Individual utility functions are u1(x11, x21) = x11 · x21 and u2(x12, x22) = x12 + x22. Find the competitive equilibrium.

Solutions

Expert Solution

At CE, MRS1= MRS2= P1/P2

As MRS2= 1, so P1/P2= 1

P1= P2= 1

so, as from demand function of individual 1

X11= M1/2*P1, X21= M1/2*P2

Endowment income of 1 at Equilibrium = 4P1 + 2P2

= 6

so at CE, x11= X21= 6/2= 3

Now from total Endowments x11+x12= 4+2= 6

So, x12= 6-3= 3

similarly , x22= (2+3)-3= 2

Rahul Sunny answered 1 year ago

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