The sole employer in the town of Silverville is a silver mine, which sells its output in a competitive market. The mine’s production function is Q = 4N − 0.125N2, which implies that the marginal product of labour is MPN = 4 − 0.25N. Suppose also that the price of silver is P = 1 (recall that the monopsonist is a price taker in the goods 7 market). The residents of Silverville have a market labour supply curve defined as follows: NS = 4W − 2.
(a) If this firm behaved like a competitive firm, how many workers would it hire? What wage would it pay its workers? Illustrate your answer with a graph. Please show detailed solving of the equations.