In an economy, there are 40 "white-collar" households, each producing 10 units of capital (and no labor); the income from each unit of capital is r. There are also 50 "blue-collar" households, each producing 20 units of labor (and no capital); the income from each unit of labor is w.
Each white-collar household's demand for energy is XW = 0.8MW/PX, where MW is income in the household. Each white-collar household's demand for food is YW = 0.2MW/PY. Each blue-collar household's demand for energy is XB = 0.5MB/PX, where MB is income in the household. Each blue-collar household's demand for food is YB = 0.5MB/PY. Energy is produced using only capital. Each unit of capital produces one unit of energy, so r is the marginal cost of energy. The supply curve for energy is described by PX = r, where PX is the price of a unit of energy. Food is produced using only labor. Each unit of labor produces one unit of food, so w is the marginal cost of food. The supply curve for labor is described by PY = w, where PY is the price of a unit of food. a) In this economy, show that the amount of labor demanded and supplied will be 1,000 units. Show also that the amount of capital demanded and supplied will be 400 units.
b) Write down the supply-equals-demand conditions for the energy and food markets.
c) In equilibrium how will the price of a unit of energy compare with the price of a unit of food?
d) In equilibrium how will the income of each white-collar family compare with the income of each blue-collar family?