Consider a pure exchange economy with two goodsk=1, 2 and two householdsi=A,B.Consider the endowmentseA=(10,2)andeB=(2,10) for households A and B, respectively. Assume the utility functions as the following:

uA(xA1,xA2)=3xA1+5xA2) and uB(xB1, xB2)=x^1/3 B1x^2/3B2.

(a) Solve the consumer problem for household A and nd the household's Marshallian demands for good 1 and 2.

(b) Same question for household B.

(c) Write down the conditions for a competitive equilibrium in this economy.

(d) Find the competitive equilibrium.

(e) Whom of the two households bene t the most from moving from consuming their endowment to a competitive equilibrium? Why?

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