Prices of rice and wool are p1 $ and p2 $ in a market. Consider that there are 40 consumers in the market in total, 30 o

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Prices of rice and wool are p1 $ and
p2 $ in a market. Consider that there are
40 consumers in the market in total, 30 of these each
with utility U1(x1, x2) =
(x1)5 (x2)3 and
income m1 $, and 15 of these each with utility
U2(x1, x2) =
x1 x2 + x1, and income
m2 $.
a) Find the ordinary demand for a consumer with
U1(x1, x2) =
(x1)5 (x2)3 .
b) Find the ordinary demand for a consumer with
U2(x1, x2) =
x1 x2.
c) Find the income elasticity of a consumer’s demand in market 2
whose utility is U2(x1, x2) =
x1 x2 + x1, evaluating
it in a setting where p1 = 4$ and
p2 = 5$ and m2 = 120$.
d) Find the aggregate demand in both markets where
p1 = 4$ and p2 = 5$
m1 = 200$ and m2 = 120$.
e) Find the own price elasticity of market 1 and evaluate it at
p1 = 4$ and p2 = 5$
m1 = 200$ and m2 = 120$.
f) Find the cross price elasticity of market 2 and evaluate it
at p1 = 4$ and p2 = 5$
m1 = 200$ and m2 = 120$.
g) Does revenue increase in market 1 due to a price increase in
a setting where p1 = 4$ and p2 = 5$
m1 = 200$ and m2 = 120$.
h) Consider the aggregate demand in market 1 as given in part
(d), and assume this also defines the relationship between price in
market 1 with respect to quantity in market 1. Define the inverse
demand function and compute marginal revenue in the market.