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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.
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