Production -Monopoly Monopoly and Factor Demands The monopolists demand for the factors of production will differ from the perfectly competitive case. en producing output y. The marginal product of the factor is MP,= Ay/Ar, the increase in output due to an increase in the input. The marginal revenue pro res the increase in revenue due to an increase in the input -it is the increase in evenue due to output changes times the increase in output due to increased factor use: MRP:= MR x Ay/Ar The marginal cost of hiring a factor is the price of the input u. A monopolist will demand the factor until the marginal benefit from doing so(MRP) equates to the marginal cost Recall that perfectly competitive firms in equilibrium hired until pAP,= w. The monopolist does not- they only hire until MRPa=w. They employ less of the factor. uction- Monopoly monopsony is a single buyer in a factor marke Suppose the monopsonist sells to a competitive market (this can be easily generalised). The firm will maximise profit: max pf(r)-wfr)r. (f(r)is the production function The firm will operate where pMP,= MCr. But the marginal cost is no longer a constant w. The firm faces the ve(much like a monopolist faces the entire demand curve). Marginal costs written as MC = u(r)(1+1/ns)where ns >0 is the price elasticity of supply. Hence marginal costs lie to the left of the supply curve. The firm will hire rat price u" They demand less, and pay a lower price for it than a competitive firm- inefficient. Minimum wage?Production — Monopoly 11 Monopoly and Factor Demands • The monopolist’s demand for the factors of production will differ from the perfectly competitive case. • Suppose there is only one factor of production, and the monopolist demands x of it when producing output y. • The marginal product of the factor is MPx = ∆y/∆x, the increase in output due to an increase in the input. The marginal revenue product measures the increase in revenue due to an increase in the input — it is the increase in revenue due to output changes times the increase in output due to increased factor use: MRPx = MR × ∆y/∆x. MRPx = p(y) ½ 1 − 1 |η| ¾ MPx ≤ p(y)MPx • The marginal cost of hiring a factor is the price of the input w. A monopolist will demand the factor until the marginal benefit from doing so (MRPx) equates to the marginal cost. • Recall that perfectly competitive firms in equilibrium hired until pMPx = w. The monopolist does not — they only hire until MRPx = w. They employ less of the factor. Production — Monopoly 12 Monopsony • A monopoly is a single seller in a market. A monopsony is a single buyer in a factor market. • Suppose the monopsonist sells to a competitive market (this can be easily generalised). • The firm will maximise profit: maxx {pf(x) − w(x)x}. (f(x) is the production function). • The firm will operate where pMPx = MCx. But the marginal cost is no longer a constant, w. The firm faces the entire supply curve (much like a monopolist faces the entire demand curve). ................................................................................................................................................................................................................................................................................ .............................................................................................................................................................................. . . ............. ............. ............. .......... . . . . . . . .......... ............. ............. ............. 0 w x MCx Supply MR = pMPx MR = MC w ∗ x ∗ • Marginal costs can be written as MCx = w(x)(1 + 1/ηS) where ηS > 0 is the price elasticity of supply. Hence marginal costs lie to the left of the supply curve. The firm will hire x ∗ at price w ∗ . • They demand less, and pay a lower price for it than a competitive firm — inefficient. Minimum wage?