A monopolist is facing a downward sloping linear market

Solution

To determine the profit-maximizing price for a monopolist facing a downward sloping linear market demand curve with zero variable cost, we need to understand how monopolists set prices. 1.      Demand Curve and Revenue : The demand curve for a monopolist is downward sloping, indicating that the price decreases as quantity increases. The monopolist will choose the quantity where marginal revenue (MR) equals marginal cost (MC). In this case, MC is zero. 2.      Marginal Revenue : The MR curve for a linear demand curve lies below the demand curve and has twice the slope of the demand curve. 3.      Profit Maximization : The monopolist maximizes profit where MR = MC. Since MC is zero, the monopolist will produce the quantity where MR = 0. For a linear demand curve, the MR curve intersects the horizontal axis (MR = 0) at the midpoint of the demand curve. This is where the price elasticity of demand is unitary elastic (elasticity = -1). Thus, the profit-maximizing price will be at the point where the demand curve is unitary elastic.