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View an economy with two goods, x and y, and a production function, z. In this economy are two types of individuals, α and β and they have an equal number of individuals. Both have the utility function U(xi, yi) = min(xi, yi), where xi and yi is consumption i= α , β of x and y.
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Each individual in α runs a business that produces good x and uses z as an input. Profit function is .
Each individual in β runs a business that produces good y and uses z as an input. Profit function is .
Initially, x and y do not exist but each individual in α and β have 10 z. Nobody alone can affect prices in the economy.
a) Find the supply functions and demand for the inputs for α and β.
b) Find equilibrium price in the economy.
