Need to know how to come up with answer given: Suppose A and B live in an exchange economy with two

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Need to know how to come up with answer given:

Suppose A and B live in an exchange economy with two goods x1 and x2. A owns 50 of both goods, and B own 250 of both goods.

A's tastes are captured by the utility function

uA(x1,x2) = x2 + 50lnx1

and B's are captured by the utility function

uB(x1,x2) = x2 + 100lnx1.

a. Let the competitive equilibrium prices be p1 and p2 respectively. Derive both consumersA????1 demand functions for both goods.

ANSWER:

A)        These preferences are translog preferences.

Demand functions are given using the equilibrium condition mRS = price ratio

MRS for A= 50/x1= p1/p2    

So x1= 50p2/p1

x2= ( M- p1*x1)/p2= (M/p2 )- 50

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