Suppose that the government of a small equatorial country requires all coconut producers to sell their output to the government. According to the text, a monopsony buyer's marginal expenditure is given by ME = P + (ΔP/ΔQ) × Q, where Q is the quantity of coconuts and P is the market price of coconuts.
a. Show that the marginal expenditure faced by the government is ME = P × (1 + 1/εs), where εs is the elasticity of supply of coconuts.
b. Show that the government's marginal expenditure on coconuts will always be greater than or equal to the price of coconuts.
c. Use the formula you derived to explain why, if the buyer's side were competitive, marginal expenditure would equal price.