Managerial Economics

Price Discrimination

Relationship between price and elasticity of demand

Marginal analysis rules says that, if MR>MC, reduce price and if MR<MC, increase price

Lerner’s Index L = 1/|e|, here L is given by (P-MC)/P which gives the equation

(P-MC)/P = 1/|e|

Here MR>MC means (P-MC)/P > 1/|e| and MR < MC means (P-MC)/P < 1/|e|

(P-MC)/P is the Current Margin of profit, 1/|e| is the Desired Margin of profit

If the current margin of profit> desired margin of profit, reduce price. If the current margin of profit < desired margin of profit, increase price.

This can be interpreted as, the more elastic the demand becomes, 1/|e| becomes smaller. This leads to decrease in price/the price increase is very slow over MC. This is because the consumer might move to another substitute as the price increases.

Pricing commonly owned substitutes

If the store owns one brand of substitute, decreasing the price on one brand increase the quantity demanded and increases the revenue

If the stores owns two brands of the substitute (Coke and Pepsi, Honda and Toyota), increasing the sales of one brand by reducing the price will steal the sales from the other brand. This is called Cannibalization.

To counter the falling MR, raising the price of both the brands (to an extent that it does not affect the sales of the other brand) will lead to higher profits.

Reason: This is because these two substitutes are treated as bundle of goods. Firms lose the incentive to drop prices as the firms in such situation is “competing with itself”.

Demand for bundle of substitutes are less elastic (EP < 1 ), than demand for individual products. For products with less elastic demand raise price (higher optimal price) to increase sales and revenue.

Note: Raise price more on the more elastic product (EP > 1). This will push the price-sensitive customers to the higher profit margin product.

For example, raise prices on both butter and margarine to sell both at a higher optimal price. Raise price more on margarine (highly elastic good) to push the price-sensitive customers to the higher profit margin good.

Pricing commonly owned compliments

If the store owns one brand of compliments, increasing the price on one brand decreases the quantity demanded and decreases the revenue

If the stores owns two brands of the compliments (concerts and parking lots, printer and cartridges), reduce the price of both the brands (to an extent that it does not affect the sales of the other brand) will lead to higher profits.

Reason: This is because these two compliments are treated as bundle of goods. Firms lose the incentive to increase prices as the firms in such situation is “competing with itself”.

Demand for bundle of compliments are more elastic (EP > 1), than demand for individual products. For products with more elastic demand reduce price (higher optimal price) to increase sales and revenue.

Revenue or Yield Management (Chapter 12, section 12.2)

Products: Hotels, stadiums, parking lots, cruise ships

Constraints: Lot of constraints one among them is space or building capacity. The costs associated with this constraint is mostly sunk or fixed cost.

Pricing Decisions: Owners have an incentive to keep adding capacity as long as

LRMR > LRMC

The owners stop building additional capacity when LRMR = LRMC

To set price, only relevant costs are included and these are short-run MR and short-run MC.

If MR > MC, then price to fill the capacity. But since they have capacity constraint they cannot reduce price to fill more room.

Optimal pricing decision in such case is to balance the cost of over pricing (lost profit of unfilled rooms/cabins) against the cost of underpricing (lower margins on all rooms/cabins).

Direct Price Discrimination

The bigger the difference between group elasticities, the more profit there is in designing a price discrimination scheme.

To price discriminate

· ID different groups with different price elasticities or different values

· Find a way to prevent arbitrage

· Firms identify members of the “low-value” group.

· Charge low-value costumers a lower price

· Prevent resale (arbitrage) to higher-value consumers.

· Identify the groups’ price elasticities and set an optimal price for each group.

Indirect Price Discrimination occurs when you:

· Cannot ID members of groups; OR cannot prevent arbitrage

· Instead, discriminate by offering two products, a higher-priced, higher-quality good and a lower-priced, lower-quality good.

· Examples: airline companies identifying leisure and business travelers, student vs full-version of software

· Adobe Photoshop (elements Vs. Professional), Matlab (student Vs. Full version)

Robinson-Patman Act

Robinson-Patman act is a part of group of laws collectively called as anti-trust law which governs competition in the U.S. Under this act, it is illegal to receive or give price discounts to the goods sold to other businesses. Robinson-Patman act, also called as the Anti-Chain Store act tries to protect the independent retailers from chain-store competitors by preventing the chains from receiving supplier discounts.

There are two ways you can defend from the Robinson-Patman lawsuit:

1. You can claim that the price-discount was cost justified

2. Price discount was given to meet the competition

Game Theory

Method of studying strategic situations in various possible outcomes involving two or more players whose actions are independent of each other’s.

Simultaneous move-game : Player move simultaneously and do not have information on each other’s move. They can predict what move other player is going to make and make a choice accordingly.

Sequential Games: No two players move at the same time. Players have several moves. Assumption is that sequential games have perfect information. In sequential move games players take turns and each player observes what the other did, before they get to decide what course of action to take.

Equilibria of sequential games, where players take turns moving, are influenced by who moves first (a potential first-mover advantage), and who can commit to a future course of action. Credible commitments are difficult to make because they require that players threaten to act in an unprintable way—against their self-interest.

Backward Induction: We start at the end and work our way up toward the beginning.

“When every player has a sequential move work your way backward and find all the optimal strategies in every given situation. These process continues backwards in time all the way until all the players’ actions and the optimal strategies have been determined. These optimal strategies in each situation is sub-game perfect Nash equilibrium. "

Dominant Strategy: A strategy that results in a best possible outcome or a highest pay-off to a given player irrespective of the strategy that the other player chooses.

Nash Equilibrium: This is a set of strategies from which each player chooses his/her best strategy, given the strategy of other players. Once the strategy has been chosen the players have no incentive to change their strategy (they will not get a better pay-off by changing the strategy).

Nash equilibrium is a solution to non-cooperative behavior among players and it is pareto inefficient.

Read the example of notes that is posted along with this document on how to find dominant strategy for each player and Nash equilibrium.

Learn how to solve for dominant strategy and Nash equilibrium. You can use the examples in the PPT or the example that is posted on Padlet with a title “Nash”

Labor Markets

The interactions between supply and demand in the market determines equilibrium price (wage rate (wage/hour)) and equilibrium quantity (the amount of labor units that is required for the production of goods and services in the economy.

Profit maximization occurs at a point where the marginal cost of hiring an additional unit of labor is equal the marginal revenue of hiring an additional unit of labor.

That is the revenue generated from the marginal productivity of the additional unit of labor is equal to the marginal cost of hiring the additional unit of labor.

Marginal Revenue Product (MRP) of labor is the additional revenue generated from additional productivity produced by hiring an additional unit of labor.

=

Marginal Factor Cost (MFC) of labor is the additional cost incurred by the firms/businesses by hiring an additional unit of labor/worker. This is the additional wage paid to the worker.

=

· A firm will hire more labor if MRP (L) > MFC (L).

· A firm will use not hire labor if MRP (L) < MFC (L).

· Profit maximization for a firm occurs at a point where for each additional level of labor results in MRP (L) = MFC (L).

Marginal revenue product curve is also the demand curve of the labor market. When there is demand for goods/services, there will be demand for productivity and the demand for labor increases.

This is why labor demand is derived demand as the demand for labor is not a direct demand but comes from the demand for goods and services .

MRP (L) shows that the demand for labor depends on two things

MRP = MR (L) * MP (L)

MR (L) – Marginal revenue generated from marginal labor productivity

MP (L) – Marginal labor productivity.

In a perfectly competitive market MRP = P, MFC = W and wage is nothing but the price we pay to hire each labor based on our demand.

Diminishing Marginal Returns

Up to a certain point each additional unit of labor yields higher productivity resulting in higher marginal revenue (MR). Then marginal revenue starts increasing at a decreasing rate reaching a point where (MRP (L) = MFC (L)) (MR = MC).

Finally MR decreases and MRP < MFC.

This is diminishing marginal returns and this occurs because of decrease in labor productivity (diminishing marginal productivity of labor)

Labor Supply: This is the total hours that workers wish to work at a given real wage rate.

Two different effects are seen due to increase in wage rates. 1. Substitution effect

· Worker will offer himself for more hours

· The price of 'leisure' will become relatively expensive

· Worker will substitute 'leisure' hours for 'work' hours

Wage rate and labor hours always has positive relationship (as wage rate increases labor hours also increases)

2. Income effect

· Higher wages lead to an increment of the individual's real income 

· People (some) continue to earn high amount of money and they start valuing leisure more than money

· Demand for leisure increases as the price of leisure drops

This leads to decrease in demand for working hours

Monopsony in labor Market

A monopsony occurs when a firm has market power in employing factors of production. A monopsony means there is one buyer and many sellers.

An example of a monopsony occurs when there is one major employer and many workers seeking to gain employment. If there is only one main employer of labor, then they have market power in setting wages and choosing how many workers to employ.

Example:

Coal mine owner in town where coal mining is primary source of employment.

Minimum Wage in Monopsony

WE

Monopsony firms would like to set wages lower than the equilibrium wages set by the market at WE.

If the price floor is below the equilibrium wage rate, then there is no economic effect.

A price floor above the equilibrium wage rate (W1) will have decrease in labor demand from L1 to L0 as the MFC of hiring labor is high with price floor.

Moral hazard and Adverse Selection

Both moral hazard and adverse selection arise from information asymmetry.

Adverse selection arise from hidden information about the type of individual you are dealing with.

Example: Hiring a sales person who is not good in sales, Risk loving applicant getting an insurance with low premium by providing false information.

Moral hazards arise from hidden actions about the type of individual you are dealing with. These people have a tendency to change their behavior after getting hired or getting an insurance.

Example: Employee who spends more time browsing/chatting after getting hired. Not installing a smoke alarm because you have home insurance/fire insurance.

Read about how to prevent Moral hazard and adverse selection behavior (Read chapters 19 and 20, especially section 20.3).

Decision making and Uncertainty

There are some phenomena where the outcomes of decisions are associated with uncertainty. The set of all the possible outcomes is known in this phenomena. To model uncertainty we use random variables to compute the expected costs and benefits of a decision.

To represent values that are uncertain,

· list the possible values the variable could take,

· assign a probability to each value, and

· compute the expected values (average outcomes) by calculating a weighted average using the probabilities as the weights.

Expected Value or Expected Monetary Value or Expected Benefits is given by

EV =

i – 1, 2, n

X – Random variable which can have ‘n’ number of values, (1, 2, .n)

P – Probability associated with each random variable, (P1, P2…... Pn)

For example,

EV =

Where,

Compute expected values of both benefits and costs of a decision

The expected value of a decision with uncertainty is given by the sum probabilities of various outcomes of a (risky) event multiplied by the expected pay-off associated with each of these outcomes.

Choose a decision when benefits > costs, otherwise do not choose.

Uncertainty is reduced by gathering information.

By modeling uncertainty, you can:

· Learn to make better decisions

· Identify the source(s) of risk in a decisions

· Compute the value of collecting more information.

Read the example of XYZ software (17.1) and tele switch (17.2) from the PPT and the text book (chapter 17).

Type I and Type II Errors

Null hypothesis (H0): Person is innocent

· Type I Error: convicting an innocent person (Rejecting a null hypothesis when it is true, false positive )

· Type II Error: not convicting a criminal (Not rejecting a null hypothesis when it is false, false negative )

Type I error: Rejecting a null hypothesis when it is true, false positive .

Type II error: Not rejecting a null hypothesis when it is false false negative.

Difference-In-Difference Estimators (DID)

· The classic DID estimator is the difference between before and after the change and also between the tratment and the control group.

· There will be unobserved factors that affect outcomes and also that changes with the treatment. Because of this there will be bias in any pre-post experiments.

· If the same unobserved factors affect the control group, then by taking the difference of the difference estimates we can remove the bias and isolate the treatment effect.

Example

When the FTC looked back at a 1998 gasoline merger in Louisville, they used their own version of a difference-in-difference estimator.

· Three control cities (Chicago, Houston, and Arlington) were used to control for demand and supply shocks that could affect price.

· The first difference was before vs. after the merger; the second difference was Louisville prices vs. prices in control cities– this allowed the FTC to isolate the effects of the merger and determine its effect.

This is a general model. Use this model to understand how the calculations are done and read the restaurant example in chapter 17 (17.3).

Possible problems with difference-in-differences estimate

Proximity: A more representative control group provides more precise estimate.

The value of conducting experiments depends on how well the control, group represents the treatment group.

Possible problems with difference-in-differences estimate

Leakage: Leakage from one group to another group leads to biased estimates.

Close proximity between control and treatment groups might also lead to leakage from one group to another.

Auctions

Auctions are simply another form of competition, like price competition or bargaining.

A Vickrey or second-price auction is a sealed-bid auction in which the high bidder wins but pays only the second-highest bid. These auctions are equivalent to oral auctions and are well suited for use on the Internet.

The optimal bidding startegy of a Vickerey auction is to bid less aggressively/to bid your true value.

Collusion or Bid Rigging : Bidders increase their profit by agreeing not to bid against one another.

Occurs more likely in open auctions and in small, frequent auctions.

If collusion is suspected,

· do not hold open auctions;

· do not hold small and frequent auctions;

· do not disclose information to bidders—do not announce who the winners are, who else may be bidding, or what the winning bids were.

Practice problems

1. Use the table provided to answer the following question.

Given that the firm only chooses to sell the high-end professional series, how should it price its product?

a. Price low and sell to both groups.

b. Price high and sell only to the professional chefs.

c. Price low and sell only to the professional chefs.

d. Price low and sell only to the home users.

Answer: assuming there's an equal number of both users, the correct answer is B.

1. Selling only to professional chefs at a high price would bring a revenue of $130 .

2. Selling to both users at a lower price of $60, would bring $120 in revenues ($60+$60).

Since the price elasticity of demand is less elastic (EP < 1) for the high-end professional series for professional chefs, the firm can price high to increase their revenue.

2. At a fair carnival roulette wheel, a player can either win $10, $30, or $80. Assuming a rational player, how much should the game owner charge the player, to maximize his own profit?

a. $30

b. $50

c. $40

d. $70

Fair carnival roulette wheel means they have equal probabilities (1/3) for all three pay-offs ($10, $30, or, $80).

Expected Value by playing the roulette wheel is = (1/3*$10) + (1/3*$30) + (1/3*$80) = $40.

To maximize his own profit the game owner charge at a point where marginal benefit equal marginal cost. Here marginal benefit (profit) is $40. So the game owner should charge each player $40 to maximize his own profit.

3. ​You raise your product price by $10 in market A but leave it unchanged in market B. Sales in A fall from 840 to 740 units per week while sales in B rise from 770 to 790 units. The Difference-in-difference estimate of the effect of the price change is:

  a.  ​80 units

  b. 100 units

  c.  ​120 units

  d. ​140 units

Difference-in-Difference Estimator is given by taking the difference in sales between pre and post introduction of advertising intensity and also between markets A and B.

The reason we get -120 units is because it follows the “law of demand” that with increase in price we get decrease in quantity demanded.

4. ​Half of all your potential customers would pay $16 for your product but the other half would only pay $10. You cannot tell them apart. Your marginal costs are $4. If you set the price at $10, the expected profit (per unit) is:

  a.  ​$3

  b. $4

  c.  ​$5

  d. ​$6

Since the price = $10, both high and low value consumers will be able to buy the product.

The expected value (revenue) = (0.5*10)+(0.5*10) = $10

Marginal cost = $4

Expected profit = $10 - $4 = $6.

5. Transcendent Technologies is deciding between developing a complicated thought-activated software, or a simple voice-activated software. Since the thought-activated software is complicated, it only has a 30% chance of actually going through to a successful launch, but would generate revenues of $50million if launched. The voice-activated software is simple and hence has a 80% chance of being launched but only generates a revenue of $10million. The complicated technology costs 10million, whereas the simple technology costs 2million.

i) What is the expected revenue from developing the complicated software?

  a.  ​$10million

  b. $15million

  c.  ​$20million

  d. ​$50million

Probability of successful launch of the complicated software = 0.3 (30%)

Revenue generated by the successful launch of the complicated software = $50,000,000

Expected Revenue = 0.3*$50,000,000 = $15,000,000 (15 million)

ii) If the firm learns that the complicated technology can be made more stable with a few tweaks increasing the cost by 5.5million and increasing the probability of a launch to 50%. Is it worth for the firm to invest the $500,000 in tweaks?

  a.  ​No, because it decreases the total expected value

  b. Yes, because it increases expected value

  c.  ​No, because it increases risk

  d. Yes, because tweaking is good

New cost = $15,500,000

Revenue = $50,000,000

P(Launch) = 0.50 (50%)

Expected Gain = $50,000,000 *0.50 = $25,000,000

Expected Profit = $25,000,000 - $15,500,000 = $9,500,000

Tweaking is good because it increases the expected value (gain) from $15 million to $25 million and also the expected profit increased from $5 million to $9.5 million.

References:

Mankiw, G.N. 2016. Principles of Macroeconomics, Eighth Edition. @ Cengage Learning.

Froeb, McCann, Shor, and ward, 2014. Managerial Economics: A Problem Solving Approach. @ Cengage Learning.