Answer

Industrial Organization Questions

Question 1 (Horizontal Product Differentiation)
Consider Hotelling’s model with a street of length 1; consumers uniformly distributed along the street; and each consumer has a transportation cost equal to 2d, where d is the distance traveled.

Suppose there are two gas stations, one located at 1/4 and the other located at 1.

[Hint: While similar to the numerical example with solutions that I have shared with you on Canvas, the questions here are a compressed version of it; you will benefit from following the detailed steps outlined in the published problem to be able to answers these questions.]

• Calculate the demand functions for both firms (fraction of consumers choosing each firm).

Assume that production costs are zero (so that firms maximizing profits is equivalent to firm
maximizing revenue). Assume that the two gas stations compete in prices and settle at a Nash
equilibrium.

Assuming the firm is located at ¼ and the second firm is located at 1.

Assuming P1 is the firm 1 price, and P2 is the firm 2 price.

Also assuming x is the consumer location who is indifferent between buying from company 1 and buying from company 2.

Hence, x must satisfy the

P1 + 2(X + 1/4) = P2 + 2(1 – X)

Therefore,

X = (P2 – P1))/ 4 + 5/8

Note: Firm 1 demand is 1 and firm 2 demand is (1 – X)

Therefore,

D1 (P1,P2) = (P2 – P1)4 + 5/8

D2 (P1,P2) = 3/8 + (P1 – P2)/4

• Calculate the Nash equilibrium price that each firm will charge for gasoline.

Firm 1 profit function is given by π1 = P1D1

Firm 2 profit function is given by π2 = P2D2

The Nash equilibrium is found by solving these equations as follows

δπ1/ δP1 = 0 and δπ2/ Δp2 = 0

δπ1/ δP1 = (P1 – P2)/ 4 + 5/4 – P1/4 = 0

δπ2/ Δp2 = 3/8 + (P1 + P2)/4 – P2/4

The solution becomes

P1 = 13/6

P2 = 11/6

• Observe if the prices charged by both firms are the same or different.

From results above, the two gas stations would be charging two different prices.

Question 2 (Exercise 14.4 from the textbook)

Empirical evidence suggests that the probability of a household switching to a different brand of breakfast cereal is increasing in the advertising intensity of that brand. However, the effect of advertising is significantly lower for households who have previously tried that brand. What does this suggest about the nature of advertising expenditures (persuasion vs information)? Answer in around 2-3 sentences.

The impact on the probability of switching is higher when the consumer failed to try the product at the beginning and it is lower in the case where the consumer already tried the product. This hypothesis is congruent with the school of thought that advertising brings an informative effect (for example, about the existence of the product). In case the advertising was only persuasive, it would be expected that the effect is similar for both, whether the customer already tried the product or not.

Question 3 (Exercise 14.3 from the textbook)

Explain how advertising expenditures with no direct informational content can increase market efficiency. Answer in around 2-3 sentences.

Although adverts do not have direct information content, the equilibrium advertising can turn out to be more efficient in comparison to the equilibrium that does not feature advertising. When companies fail to advertise their products, even if such company’s manufactures high quality products, they do not have production incentive, and ultimately, such companies fail to differentiate themselves. In our case, the company products will be ex-ante, meaning that they will just be like the companies producing low quality products. In this respect, if the customers prefer high quality goods or services, even in a situation where a company saves costs in its advertising, the company overall efficiency impact would still be negative due to the fat that the product is not properly exposed to the consumers who should be having it.