Question

1. Consider a wholesaler and a retailer selling designer handbags. Each has market power. The wholesaler sells designer hadbags to the retailer, which then sells the handbags to consumers. The demand for handbags is captured by P = 24-Q. Assume that the marginal cost of producing a handbag is constant (MC=$8). Consider the following scenarios:

a) Suppose that the retailer is the only firm and that it can produce the handbags it sells (there is no wholesaler here). How many handbags will be produced and what price will be charged? Draw a graph and show these points on the diagram.

b) Now suppose that the retailer cannot produce handbags and must instead buy them from the wholesaler. The wholesaler charges the downstream firm $16 per handbag. How many handbags will the retailer purchase and sell, and what price will the retailer charge?

2. If the wholesaler and retailer in problem 1 merged, what would be the effect on overall social surplus?

3. Discuss the problem of double marginalization. What is it? What causes it? How is it mitigated by a vertical merger?

4. Define first degree price discrimination, second degree price discrimination, and third degree price discrimination. Provide an example of each.

5. We have seen how monopolistic industries can result in a deadweight loss relevant to the competitive outcome. Consider the case of a monopolist engaging in first degree (perfect) price discrimination. How do you think the profits of the monopolist and overall social welfare are affected compared to the case where the monopolist sets a single monopoly price? (Hint: try drawing a simple diagram in both cases).

Answer 1

It is given that the demand for handbags is P= 24-Q where P is the price and Q is the quantity.

Therefore, Total Revenue (TR) = P*Q = 24Q-Q²

Therefore Marginal Revenue (MR) = dTR/dQ = 24-2Q

The Marginal cost of PRODUCTION is given as $8.

The profit maximizing condition under monopoly requires Marginal Revenue (MR)=Marginal Cost (MC).

1) a) When the retailer produces its own bags and there is no wholesaler, the retailer is the monopolist. Therefore, profit maximization condition requires:

         24-2Q = 8 or 2Q= 16 or Q= 8.

Therefore, P=24-Q or P= 24-8 = $16.

Thus, when there is no wholesaler, 8 bags will be produced and sold and a price of $16 each. This is shown in fig 1. The AR curve is the price curve for the Monopolist and the MR curve is half of the AR curve. The intersection of MR and MC gives a quantity of 8 bags and its corresponding AR curve gives a price of $16.

b) When the retailer cannot produce bags, the wholesaler produces bags and in the bag production business, the wholesaler acts as a monopolist. Therefore the above conditions apply to the wholesaler and he charges a price of $16 to the retailer. Since the retailer CANNOT produce handbags, MC = $8 for PRODUCTION of handbags is not applicable to the retailer (which is the downstream firm because it is below the wholesaler). However, the price at which it buys one handbag ($16) now becomes its MC. The demand and MR curves do not change.

Thus, at profit maximizing level, MR= MC implies

24-2Q= 16 or 2Q = 8 or Q=4.

Therefore, P= 24-Q or P= 24-4 or P=20.

Thus, when the retailer is a downstream firm, it purchases and sells 4 handbags and charges $20 per handbag from each of its customers.

2) When the wholesaler and the retailer merge, then the wholesaler sells the handbags to the retailer at its MC of $8. Thus the retailer for profit maximization follows: MR = MC (under merging) i.e. 24-2Q = 8 or 2Q= 16 or Q= 8.

Therefore, P=24-Q or P= 24-8 = $16.

Under this situation, the overall social surplus (CS + PS) is greater than the overall social surplus without merging. The results with integration are the same as the results in 1(a) therefore its reference can be made with fig 1. The diagram without integration (corresponding to 1(b)) is drawn in fig 2.

In Fig 1, the Consumer’s Surplus (CS) is given by the area of the triangle ABC shaded in green. The Producer’s Surplus (PS) is given by the area of the quadrilateral BCED shaded in yellow. In Fig 2, the Consumer’s Surplus (CS) is given by the area of the triangle A’B’C’ shaded in green. The Producer’s Surplus (PS) is given by the area of the quadrilateral B’C’E’D’ shaded in yellow.

Without even going into numerical calculations, it is clear that the overall social surplus (CS+PS) is greater in the case of Merging (in Fig 1) as it constitutes a bigger area than the overall social surplus without Merging (In fig 2).

3) The problem of double marginalization occurs when there are two levels of separate firms that a product has to pass through, before reaching the hands of a consumer. From this example, when the wholesaler and retailer do not merge, then the wholesaler initially produces at a level where its MR= MC. Thus, even though its MC is $8 (MC_U), at the level where MR=MC, the price of the handbag is $16 (P_U)

This handbag acts as an input to the retailer and its MC in turn becomes $16 (MC_D). However it too follows the same profit maximizing principle of MR=MC and at that level, produces and sells only 4 handbags at $20 (P_D) each. Thus, when both the upstream and the downstream firm sells handbags at a marked price much above the Marginal cost (P_U> MC_U and P_D> MC_D) then, there arises the problem of double marginalization.

The cause of double marginalization is non-integration of firms producing and selling the same product in a step-by-step process. This is because, when firms do not integrate, they act as separate identities who are interested in their OWN PROFIT MAXIMIZATION at the expense of the ones below them.

This problem is solved by a Vertical Merger because a vertical merger implies merging or integration of firms at different levels of production whose joint aim is to maximize profit. The merged firm now acts as 1 whole firm as opposed to separate firms in the previous case. The motive of the firm is still profit maximization, but since the Upstream and Downstream firms are the SAME entity now, the upstream DOES NOT PRICE THE HANDBAGS AT A MARKED PRICE ABOVE THE MC. Rather, it sells the handbags to the retailer at the MC and price is marked up only once by the retailer which results in sale of a higher number of handbags and generation of higher total revenue. The problem of double marginalization is also mitigated as only the retailer charges a price above the MC whereas the wholesaler behaves like a perfect competitor and prices its handbags at its marginal cost.

4) Price discrimination refers to the act of charging different consumers, different prices for the same commodity. It is of three main types:

First degree price discrimination is defined as the act of charging each consumer THE MAXIMUM PRICE that he/she is willing to pay for each additional unit of commodity purchased. This is also known as Perfect Price Discrimination where the entire consumer’s surplusis extracted by the monopolist. E.g. The last 10 tickets to the most awaited concert of the season will be given to those buyers who offer to pay the highest price for them. Every buyer quotes his/her maximum willingness to pay and those who outbid the others, purchase the tickets,

Second degree price discrimination is where the monopolist charges different prices for different quantities of goods or services consumed. The segregation of prices is done on the basis of quantities consumed. In this case, the buyer knows that there are different consumers, but doesn’t know which consumer prefers to be in which type or group. Thus there is a ‘self selection constraint’ in this type of price discrimination where the consumer ‘self selects’ the price group he wants to place himself in, on the basis of quantity consumed. For example, ‘bulk discounts’ where a consumer buying in bulk will get more discount and pay less price for more quantity of the SAME GOOD.

Third degree price discrimination involves charging different groups of consumers different prices for the SAME product where the segregation of consumers into groups have been done on the basis of observable characteristics. Here, unlike in the previous case, the seller knows which consumer falls into which group and charges different prices accordingly. For example, the same much awaited concert of the season can have different prices of tickets based on age group. For example, under-21 tickets and senior citizen tickets can be cheaper than tickets for those aged above 21 and below 65.

5) The fact that monopolist operating at a single price causes deadweight loss is clear from figure A where the deadweight loss is labelled DWL. However, a price discriminating monopolist doesn’t operate at a single price. The act of perfect price discrimination is shown in Fig B where economic profit is maximized, all consumer’s surplus is converted into profit or producer’s surplus and deadweight loss is completely eliminated. Thus, overall social welfare is maximized. The situation is definitely not equitable, but it is efficient as the loss in consumer’s surplus gets converted into a gain in producer’s surplus and no amount goes into deadweight loss of the society.