Managerial Economics - Game Theory and Pricing Strategies

Many service industries such as restaurants, night clubs, movie theatres, and hair dressers experience much higher demand during weekends compared to weekdays. Explain a pricing strategy which would increase profits compared to a single price profit maximizing strategy. Be sure to include a graph which explains your demand, marginal revenue, and marginal cost.

1. When the demand during peak times is so high that the capacity for the firm cannot serve all customers at the same price, the profitable thing for the firm to do is engage in peak-load pricing. Peak-loading involves charging a higher price during peak times. The graph below illustrates peak-loading. MC is constant up to Qhigh where the firm is operating at full capacity and cannot produce any more units. The two demand curves correspond to peak and off-peak demand for a product where Dlow is the off-peak and Dhigh is the high peak. In general, where there are two types of demand, a firm will maximize profits by charging different prices to different groups ("groups" are those who purchase at different times). Demand during low-peak times is such that MR = MC at Qlow. Thus the profit maximizing price during those times is Plow. In contrast, during high peak times, MR = MC at Qhigh which corresponds to full capacity. The profit-maximizing price during high-peaks is Phigh.

Transfer Pricing

A firm often has to price items that the firm produces and uses internally, commonly referred to as intermediate goods. How should these intermediate goods be priced? If a perfectly competitive market exists for such goods, the firm should use that market-determined price. If a perfectly competitive market does not exist, the transfer price is a function of the marginal costs and revenues of the different divisions in the firm.

Two part pricing

A monopolistic firm can also increase its profits by requiring the customer to pay an initial fee for the right to buy its product, plus a per-unit charge for each unit purchased. This is also known as a two-part tariff. Examples include telephone companies that charge a monthly fee plus an amount per call made, and golf courses and health clubs that charge an "initiation fee" in addition to other user fees. (See Figure 11-2 "Comparisons of Standard Monopoly Pricing and Two-Part Pricing" on page 352 of your textbook.) Under two-part pricing, the monopolist charges a per-unit price equal to its marginal cost, plus a fixed fee equal to the consumer surplus each customer receives at this per-unit price. By so doing, the monopolist is able to extract all consumer surplus from consumers, just like under first-degree price discrimination.

Block Pricing

Another way for a monopolistic firm to increase its profits is to engage in block pricing, where identical products are grouped together and sold as a package, thus forcing the customer to make an all-or-nothing decision to purchase. Examples include the sale of beer in six-packs or toilet paper rolls in packs of twenty-four. The profit-maximizing price on a package is the total value the consumer receives for the package, including the consumer surplus.

Commodity Bundling

Commodity bundling can increase profits when buyers differ in terms of the amounts they are willing to pay for multiple products sold by the firm. Some restaurants, for example, have special deals where for a set price one gets a three-course meal. Travel agencies advertise "package deals" that include air travel and hotels. Your textbook provides a very good numerical example of how commodity bundling works on pages 356-357

Profit-Maximizing Markup for Monopoly and Monopolistic Competition

The price that maximizes profit is given by: P = [ (Ef/(1+Ef) ] * MC where Ef is the own-price elasticity of demand for the firm's product and MC is the firm's marginal cost. The term in brackets is the optimal markup factor.

Simultaneous-move game

Game in which each player makes decisions without knowledge of the other players' decisions

One-shot game

Game in which the underlying game is played only once.

Markup Pricing for Cournot Oligopoly

In a Cournot oligopoly, each firm assumes its rivals will keep their output constant if it changes its own. In an industry with N Cournot oligopolists selling identical products, the elasticity of demand faced by each firm is N times the market elasticity of demand: EF = NEM If all the firms face identical costs, the profit-maximizing price can be written as: P = {NEM/(1 + NEM)} MC where N is the number of firms in the industry and EM is the market elasticity of demand (see page 401 of your textbook for the derivation of the equation).

Why is it impossible for any price maker, including a monopolist, to practice firstdegree price discrimination?

Its impossible to know the consumer valuation for each unit of the same product where many units are bought. If a single buyer buys only one unit there will likely be no consumer surplus, and first-degree discrimination has no relevance since the goal of a monopolist is to increase profits by taking away the consumer surplus.

Assume that a monopoly has a linear demand curve. If it is charging the profit maximizing price, will the demand for its product at that price be elastic or inelastic?

MR for a monopolist lies below the demand curve and exactly halfway between the demand curve and vertical axis. This means that for a monopolist, MR is less than the price charge for a good. The demand must be elastic because it is located in the upper elastic half of the linear demand curve and because MC is positive. Since MC is positive then MR must also be positive where they equal each other. MR can only be positive in the elastic half of the linear demand curve. Why? In addition, if demand was inelastic a price increase would increase TR since the price increase is proportionately greater than the fall in quantity demanded, and reduce TC since the quantity produced is smaller at the higher price, thereby increasing profits, TR-TC.

Peak load pricing

Peak-load pricing refers to the practice of charging different prices at different points in time. The demand for some goods or services increases drastically during certain times of the day. For example, toll roads experience more traffic during rush hours than at other times, and telephone companies need more capacity during business hours than at night. The purpose here is not to capture consumer surplus but to increase efficiency by charging a higher price during peak periods when marginal cost is higher. Of course, it is also more profitable than charging a single price at all times. Under peak-load pricing, the monopolist equates marginal revenue to marginal cost for each time period to arrive at the prices to be charged. Since demand is higher during peak periods and so is the marginal cost, a higher price is charged during peak periods than during off-peak hours (see Figure 11-5 "Peak-Load Pricing" on page 359 of your textbook).

Simultaneous move, one shot games

Player A can choose between two strategies: Up or Down. Player B can choose Left or Right. In quadrant A, A chooses Up and B chooses Left: A makes 10 and B makes 20. In quadrant B, A chooses Up and B chooses Right: A makes 15 and B makes 8. Given that each player gets to make one and only one decision, and all players must make their decisions at the same time, what is the optimal strategy? A dominant strategy is a strategy that results in the highest payoff, regardless of the actions of the other players. For Player A, the dominant strategy is Up. Why? If Player B chooses Left, Player A makes 10, better than -10 if he chooses Down. If Player B chooses Right, the best choice for Player A is still Up (15 is better than 10). Not all games have a dominant strategy for each player or firm. In the above example, Player B does not have a dominant strategy (see "Demonstration Problems 10-1" and 10-2 on pages 305-306 of your textbook). Instead, Player B has a secure strategy, one that guarantees the highest payoff given the worst possible scenarios. When a player does not have a dominant strategy, the player should look at the game from the rival's perspective. If the rival has a dominant strategy, the player should anticipate that the rival will play it.

You have been asked by your boss to report on the expected profits from a single price strategy compared with a two-part pricing strategy. The estimated demand for the firm's product is: Qd = 400 - 0.2P . Per unit cost is estimated as constant at $1,000.00. Provide a report which explains the profits from a single price profit maximizing strategy with a two-part profit maximizing strategy involving a fixed fee plus a per unit fee. Assume that total fixed cost is $30,000. What is the optimal fixed fee? Why does the two-part pricing policy increase total profits?

Profit increases to $70,000

Cross subsidies

Whenever a multiproduct firm has cost complementarities (recall economies of scope learned in Chapter 5) and demand for a group of products is interdependent, the firm can use profits earned from the sale of one product to subsidize sales of a related product. Your textbook illustrates this practice with the way Adobe sells two of its products: they offer Adobe Reader free but consumers must purchase Adobe Acrobat.

How is first-degree price discrimination different from second-degree price discrimination?

a. First and second are different in the sense that first takes away all of the CS whereas second only takes some of the CS. First degree charges each consumer the maximum price he or she is willing to pay for each unit of the good purchased. By adopting this strategy, a firm extracts all the consumer surplus from consumers and thus earns the highest possible profits. This strategy is impossible to implement as it requires the firm to know precisely the maximum price each consumer is willing and able to pay for each unit of the firm's product. Second degree is the practice of posting a discrete schedule of declining prices for different ranges of quantities. Often only two prices, The advantage of this strategy is that a firm can extract some of the consumer surplus from consumers without needing to know beforehand the valuations of the consumers who will chose to purchase small amounts and thus are willing to pau at a higher price per unit.

First Degree Discrimination

each customer is charged the maximum he or she is willing to pay for each unit of the product. Recall that the difference between what a consumer is willing to pay and what he or she actually pays is consumer surplus. There is no consumer surplus under first-degree price discrimination; it all goes to the monopoly. An example would be goods sold on eBay. Where several units of the good are bought, it is almost impossible to implement first-degree price discrimination since the price the consumer is willing to pay falls with each additional unit bought.

Nash Equilibrium

each firm chooses a strategy that is its best choice given what its rivals do. In the above example, Player A has a dominant strategy (Up) and Player B has a secure strategy (Right). But the Nash equilibrium is Up for Player A and Left for Player B.

Price Discrimination

is the practice of selling the same good or service at different prices to different customers or to the same customer, for different units, when the differences are not cost justified. There are three types of price discrimination (classified similarly to murder is in the courts!): first-degree, second-degree, and third-degree.

Second Degree Discrimination

several different prices are charged for different ranges or groups of output. An example would be the pricing of hydro where a higher rate is charged for the first hundred kilowatt-hours used than on subsequent units. We observe many examples of second-degree price discrimination such as $10 for one unit and $16 for two units. The second unit is effectively sold for $6.

Third degree discrimination

the market is segmented into two or more groups and each group is then charged a different price to maximize profits (with all members in each group paying the same price). The firm must be able to identify differences in elasticities of demand and prevent resale by the consumers charged the lower prices.