Consider a competitive economy consisting of many farmers and many tailors. The number of farmers is equal to the number

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Consider a competitive economy consisting of many farmers and
many tailors. The number of farmers is equal to the number of
tailors. Farmers are identical. Each farmer has 10 units of food
(F) but no clothing (C). Tailors are also identical. Each tailor
has 20 units of clothing but no food. Suppose each person has the
utility function U = FC . The price of clothing is always £1. What
is the equilibrium price for food? Explain your answer.
(a) If the price of food is $3, does this price support a
competitive equilibrium? Explain. [Hint: Solve for the optimal
consumption bundle for a farmer and the optimal consumption bundle
for a tailor first. Use this information to determine whether the
prices lead to a competitive equilibrium.]
(b) If not, what will happen to the price of food?
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