The inverse demand curve is given by and a monopolist
has a fixed supply of 4 units of a good available.
How much will it sell and what price will it set?
a) What would be the price and output in a competitive market with these demand and supply characteristics?
b) What would happen if the monopolist had 6 units of the good available? (Assume free disposal.)
a) In a competitive market, the price and output would be determined by the intersection of the demand and supply curves. The demand curve is given by P = 20 - Q and the supply curve is given by Q = 4. The intersection of these two curves occurs at P = 16 and Q = 4. Therefore, in a competitive market, the price would be 16 and the output would be 4.
b) If the monopolist had 6 units of the good available, the price would be higher and the output would be lower than in a competitive market. The monopolist would set the price at the level that maximizes its profits, which is the intersection of the demand curve and the marginal cost curve. The marginal cost curve is given by MC = 0, since the monopolist has a fixed supply of 6 units. The intersection of the demand curve and the marginal cost curve occurs at P = 18 and Q = 3. Therefore, the monopolist would set the price at 18 and the output at 3.