Consider a society consisting of just a farmer and a tailor. The farmer has 10 units of food but no clothing. The tailor has 20 units of clothing but no food. Suppose each has the utility function U = F ? C. The price of clothing is always $1
If the price of food is $3, does a competitive equilibrium exist? If not, what will happen to the price of food?
If the price of food is $3, the farmer's initial wealth is $30. His budget line is 30 = 3F + C. His budget line is tangent to an indifference curve when C/F = 3. Substituting yields 30 = 6F or F = 5 and C = 15. The tailor's budget line is 20 = 3F + C. His budget line is tangent to an indifference curve when C/F = 3. Substituting yields 20 = 6F or F = 3.33 and C = 10. In total 8.33 units of food and 25 units of clothing are demanded. There is excess demand for clothing and excess supply of food. The price of food will fall. When the price of food is $2, both markets clear.
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