Chapter 1Figure It Out 10.1

To find the profit-maximizing output, first find marginal revenue, and then equate marginal revenue and marginal cost. Marginal revenue starts at the same point as the inverse demand but has twice the slope, so MR = 100 – 20Q. Setting MR = MC, 100 – 20Q = 10 + 10Q. So, Q = 3. Substitute 3 for Q in the demand curve to find the profit-maximizing price, $70. For further review see section “Profit Maximization for a Firm with Market Power”.

Consumer surplus is the area above the price and below the demand curve, shown as area A in the graph. That triangle is $30 tall and 3 units wide, so its area is 0.5 × $30 × 3, or $45.
Producer surplus is the area below the price and above the supply curve, shown as areas B + C in the graph. To determine those areas, plug 3 units of output into the marginal cost function to find that MC = $40. So, area C is a triangle $30 tall and 3 units wide, for an area of 0.5 × $30 × 3, or $45. Area B is a rectangle $30 tall and 3 units wide, or $30 × 3 = $90. Therefore, areas B + C = $90 + $45 = $135.
The deadweight loss is surplus that would be created under perfect competition but not with a market in which a firm has market power. That area is shown as D in the graph. To find area D, find the perfectly competitive output level by equating marginal cost and demand: 10 + 10Q = 100 – 10Q, or Q = 4.5. So, area D is a triangle $30 tall and 1.5 units wide, for an area of 0.5 × $30 × 1.5, or $22.50. For further review see section “The Winners and Losers from Market Power”.

A firm practicing perfect price discrimination will sell any unit for which the price the buyer is willing to pay (represented by the demand curve) is greater than or equal to the marginal cost of production, and will stop selling when P = MC. That occurs where the demand curve intersects marginal cost, or when 100 – 10Q = 10 + 10Q. Solve to find that Q = 4.5. For further review see section “Direct Price Discrimination I: Perfect/First-Degree Price Discrimination”.

A perfectly price-discriminating firm charges each buyer his or her maximum willingness to pay, so each consumer receives zero surplus.

Perfect/First-Degree Price Discrimination”.