Use the demand schedule that follows to calculate total revenue and marginal revenue at each quantity. Plot the demand, total-revenue, and marginal-revenue curves and explain the relationships between them. Explain why the marginal revenue of the fourth unit of output is $3.50, even though its price is $5.00. Use Chapter 20's total-revenue test for price elasticity to designate the elastic and inelastic segments of your graphed demand curve. What generalization can you make regarding the relationship between marginal revenue and elasticity of demand? Suppose the marginal cost of successive units of output were zero. What output would the profit-seeking firm produce? Finally, use your analysis to explain why a monopolist would never produce in the inelastic region of demand.
ANSWER:
Total revenue, in order from Q = 0: 0; $6.50; $12.00; $16.50; $20.00; $22.50; $24.00; $24.50; $24.00; $22.50. Marginal revenue in order from Q = 1: $6.50; $5.50; $4.50; $3.50; $2.50; $1.50; $.50; -$1.50. See the accompanying graph. Because TR is increasing at a diminishing rate, MR is declining. When TR turns downward, MR becomes negative. Marginal revenue is below D because to sell an extra unit, the monopolist must lower the price on the marginal unit as well as on each of the preceding units sold. Four units sell for $5.00 each, but three of these four could have been sold for $5.50 had the monopolist been satisfied to sell only three. Having decided to sell four, the monopolist had to lower the price of the first three from $5.50 to $5.00, sacrificing $.50 on each for a total of $1.50. This "loss" of $1.50 explains the difference between the $5.00 price obtained on the fourth unit of output and its marginal revenue of $3.50. Demand is elastic from P = $6.50 to P = $3.50, a range where TR is rising. The curve is of unitary elasticity at P = $3.50, where TR is at its maximum. The curve is inelastic from then on as the price continues to decrease and TR is falling. When MR is positive, demand is elastic. When MR is zero, demand is of unitary elasticity. When MR is negative, demand is inelastic. If MC is zero, the monopolist should produce 7 units where MR is also zero. It would never produce where demand is inelastic because MR is negative there while MC is positive.
Suppose a pure monopolist is faced with the demand schedule shown below and the same cost data as the competitive producer discussed in question 4 at the end of Chapter 23. Calculate the missing total- and marginal-revenue amounts, and determine the profit-maximizing price and profit-earning output for this monopolist. What is the monopolist's profit? Verify your answer graphically and by comparing total revenue and total cost.
ANSWER:
Total revenue data, top to bottom, in dollars: 0: 100; 166; 213; 252; 275; 288; 294; 296; 297; 290. Marginal revenue data, top to bottom, in dollars: 100; 66; 47; 39; 23; 13; 6; 2; 1; -7.
Price = $63; output = 4; profit = $42 [= 4($63 - 52.50)]. Your graph should have the same general appearance as Figure 24-4. At Q =4, TR = $252 and TC = $210 [= 4($52.50)].
24-6
If the firm described in question 5 could engage in perfect price discrimination, what would be the level of output? Of profits? Draw a diagram showing the relevant demand, marginal-revenue, average-total-cost, and marginal-cost curves and the equilibrium price and output for a nondiscriminating monopolist. Use the same diagram to show the equilibrium position of a monopolist that is able to practice perfect price discrimination. Compare equilibrium outputs, total revenues, economic profits, and consumer prices in the two cases. Comment on the economic desirability of price discrimination.
ANSWER:
Perfect price discrimination: Output = 6. TR would be $420 (= $100 + $83 + $71 + $63 + $55 + $48). TC would be $285 [= 6(47.50)]. Profit would be $135 (= $420 - $285).
Your single diagram should combine Figure 24-8a and 24-8b in the chapter. The discriminating monopolist faces a demand curve that is also its MR curve. It will sell the first unit at f in Figure 24-8b and then sell each successive unit at lower prices (as shown on the demand curve) as it moves to Q2 units, where D (= MR) = MC. Discriminating monopolist: Greater output; total revenue, and profits. Some consumers will pay a higher price under discriminating monopoly than with nondiscriminating monopoly; others, a lower price. Good features: greater output and improved allocative efficiency. Bad feature: More income is transferred from consumers to the monopolist.
24-12
It has been proposed that natural monopolists should be allowed to determine their profit-maximizing outputs and prices and then government should tax their profits away and distribute them to consumers in proportion to their purchases from the monopoly. Is this proposal as socially desirable as requiring monopolists to equate price with marginal cost or average total cost?
ANSWER:
No, the proposal does not consider that the output of the natural monopolist would still be at the suboptimal level where P > MC. Too little would be produced and there would be an underallocation of resources. Theoretically, it would be more desirable to force the natural monopolist to charge a price equal to marginal cost and subsidize any losses. Even setting price equal to ATC would be an improvement over this proposal. This fair-return pricing would allow for a normal profit and ensure greater production than the proposal would.
