Consider the market for wheat (measured in bushels) in the US. For simplicity, suppose that all wheat farmers have the same cost function, given by

C(q)=27+4q³

The market demand for wheat is given by

Q = 225 p

a) Suppose that each wheat farmer has a neglible effect on total supply, and is thus a price-taker. Find the profit-maximizing condition of a wheat farmer. Describe in words what this condition is saying (i.e. why this condition must hold if the farmer is maximizing profits).

b) How many wheat farmers will there be in a long-run perfectly competitive equilibrium?

c) An innovation to farming technology changes the cost function to

C(q)=8+4q³

Calculate the short-run profits of each wheat farmer. Comment on i) the equilibrium price and quantity vs the ones from part b) and ii) what explains any difference in profit in part c) vs b)

d) Calculate the long-run change in the number of wheat farmers. Explain in words what drives this change.

e) Without explicitly calculating welfare, give an argument for whether over- all welfare is higher or lower in the long-run equilibrium of part d) vs the short- run equilibrium of part c).