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(x^i, yⁱ) = min(xⁱ, yⁱ), where xⁱ and yⁱ is consumption i= α , β of x and y.

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.