Homework Answers
(a) Optimal demand is determined where MRS = p1/p2
MRS = MU1/MU2 =
So, MRS = p1/p2 gives,
ax2/x1 = p1/p2
So, x1 = ax2*(p2/p1)
Budget constraint: p1x1 + p2x2 = m
So, p1*ax2*(p2/p1) + p2x2 = m
So, ap2x2 + p2x2 = m
So, (ap2 + p2)x2 = m
So, x2 = m/(ap2 + p2)
x1 = ax2*(p2/p1) = a*(p2/p1)*m/(ap2 + p2) = a*(p2/p1)*m/p2(a +
1) = am/(ap1 + p1)
So, x1 = am/(ap1 + p1)
b. Demand of type A consumer for good 1, A = am/(ap1 + p1) =
1*m/(1*p1 + p1) = m/2p1
Demand of type B consumer for good 1, B = am/(ap1 + p1) = 2m/(2p1 +
p1) = 2m/3p1
Total demand for x1 = A + 2B = (m/2p1) + 2*(2m/3p1) = (m/2p1) +
(4m/3p1) = (3m + 8m)/6p1 = 11m/6p1
Total demand = 11m/6p1
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