Seminar 5 solutions Ethan O’Leary∗ September 2021 1 Q1 1.1 Part a) Our given market demand curve is P = 12−Q for yeast and there is one present firm *Gestur.* The total revenue obtained by *Gestur* for any quantity at any given price is hence: T R = (12 − Q) · Q T R = 12Q − Q2 The marginal revenue is hence defined by: MR = d(T R) = 12 − 2Q dQ Since monopolistic firms produce the profit maximising quantity, Q∗ , defined by the point at which the marginal revenue is equal to the marginal cost, we compute: MR = MC 12 − 2Q∗ = 0 Q∗ = 6 According to the market demand equation, the profit maximising price, P ∗ , is given by: P ∗ = 12 − Q∗ = 12 − 6 = 6 ∗ 41643@student.hhs.se 1 Hence the maximised profit is π ∗ = T R − T C = P ∗ Q∗ − c = 36 where c is C) some constant such that d(T = 0. In other words, there is only a fixed cost dQ equal to some constant c (which could be zero). From herein, we assume for simplicity that c = 0. See below for a diagram. 1.2 Part b) The producer surplus in this case is defined by the profit (P ∗ − M C) · Q∗ which is computed above to be 36. From the diagram below, one can see that the consumer surplus is defined as the triangle above the price set P ∗ that is bounded above by the market demand curve. The area of such is 12 (P M AX − P ∗ )Q∗ = 1 M AX is the price at which the demand curve intersects 2 · 6 · 6 = 18 where P the vertical axis (here it is 12). Further, the deadweight loss is computed as the remaining triangle such that DW L = 12 · P ∗ · (QM AX − Q∗ ) = 18 where QM AX is the point at which the market demand curve intersects the horizontal axis. The presence of this non-zero deadweight loss is a signal of market inefficiency caused by a price setting monopolist. A diagram is included below. 2 1.3 Part c) In a Cournot duopoly we have two firms producing homogeneous (the same) goods facing a common market demand with individual cost functions. Thus firms form reaction functions which intuitively show **the profit maximising quantity the firm should produce given the quantity produced by the other firm**. Clearly then we expect the reaction function (RF) to be a function in the form qi∗ = f (qj ). We formulate this by incorporating the two firms’ individual outputs into the market output such that Q = qG + qJ i.e. the market output is the output of *Gestur* plus the output of *Jaer.* This allows us to rewrite the market demand curve as: P = 12 − Q = 12 − qG − qJ As per our assumption in part a), we assume no fixed costs such that T CG = T CJ = 0. Thus both firms facing the same demand and cost functions will face the same profit maximisation problem where Profit π for firm i is defined as πi = (12 − Q) · qi . To solve this for *Gestur,* we acknowledge the profit maximisation problem which can be written as: max πG = (12 − qG − qJ )qG qG ≥0 To find a maximum point, we differentiate the profit function subject to the variable which *Gestur* is choosing: it’s output quantity, and set this to equal zero: ∂πG = 12 − 2qG − qJ = 0 ∂qG [NOTE: the keen eyed among you will wonder why I have used the symbol ∂ above instead of d. The reason is that there is more than one variable in the equation for profits of *Gestur.* The ∂ symbol states that we differentiate the profit function with respect to some variable (here qG ) while keeping all other variables constant (so we can treat qJ in this example just like a constant)]. ∗ , we have: Rearranging the above equation to compute qG ∗ 2qG = 12 − qJ 1 ∗ qG = 6 − qJ 2 Which tells us the optimal profit maximising quantity that *Gestur* should produce given any output produced by *Jaer.* Note that since *Jaer* has an identical profit maximising problem, we can write *Jaer’s* reaction function as: 1 qJ∗ = 6 − qG 2 We can draw these two reaction functions on one diagram to show our optimal point at where these two cross: 3 Substituting this into the reaction function for *Gestur*, we can compute: 1 ∗ 1 ∗ 1 ∗ ) = 3 + qG qG = 6 − (6 − qG 2 2 4 3 ∗ q =3 4 G ∗ qG =4 Since we have symmetrical problems, we also have qJ∗ = 4 and thus market price is P ∗ = 12 − qG − qJ = 4. Thus each individual firm has a profit of πiC = P ∗ · qi∗ = 16 which is less than the monopolisation profit. In this case, we expect that the deadweight loss is reduced from the previous diagram. From the below diagram, we allow *Gestur* to produce 4 units as it would want to according to its marginal revenue curve. This leaves the rest of the market demand curve open for *Jaer* to conquer. Since the two firms are colluding they both price at P ∗ = 4 given the output level set individually at 4 units per firm and thus the consumer surplus has increased while the deadweight loss has decreased. Note that the producer surplus has also decreased in whole C and has decreased for each individual firm πG + πJC = 32 < 36. 4 marginal cost changes for Jaer, meaning that his profit is no longer (P x Qj)Qj, but (P x Qj)Qj—2Qj This is because the cost changes for one firm, and their reaction function will change. And there is a new Cournot eq. 1.4 Part d) In part d, firms no longer have homogeneous cost functions. As such while *Gestur*’s profit function remains at πG = (12 − Q)qG , the profit function of *Jaer* is now πJ = (12 − Q)qJ − 2qJ = (12 − qG − qJ )qJ − 2qJ since total cost is 2qJ for *Jaer.* Hence, we reaction function for *Gestur* is unchanged, but we must compute a new reaction function for *Jear* by differentiating the profit function and setting it to the value of zero: ∂πJ ∂qJ = 12 − qG − 2qJ − 2 = 0 Rearranging the right hand side, one obtains: 2qJ∗ = 10 − qG 1 qJ∗ = 5 − qG 2 By substituting this into the original reaction function for *Gestur* computed in part c, one obtains the profit maximising output for *Gestur:* 1 1 ∗ ∗ qG = 6 − (5 − qG ) 2 2 5 ∗ qG = 7 1 ∗ + q 2 4 G 14 >4 3 Further, the profit maximising output of *Jaer is now:* ∗ qG = 1 14 7 8 =5− = <4 2 3 3 3 Hence since *Jaer* faces a higher per unit cost than *Gestur, Gestur* is able to capture a higher market share. This reflects the notion of economic efficiency - since it is cheaper for *Gestur* to produce yeast, it is a more efficient use of resources to allocate a greater share of production to *Gestur.* 8 14 ∗ − qJ∗ = 12 − 14 Here the market price will be P ∗ = 12 − qG 3 − 3 = 3 > 4 thus since the total quantity supplied to the market is less than the case in part c, the market price set is higher and the aggregate profits are: qJ∗ = 5 − 8 266 14 14 8 14 + −2 = < 32 3 3 3 3 3 9 Thus profits are lower in this case indicating a reduction in the producer surplus. In this case, the deadweight loss increases also indicating that the greater the marginal cost of firms, the greater the inefficiency in the case of collusion power (price setting). π = πG + πJ = 6 7 2 2.1 Q2 Part a) In the case where a low income country (e.g. Thailand) demands a small quantity of goods at every price but a higher income country (e.g. Germany) demands a proportionally larger quantity of goods at every price, a market-set price formed by an aggregated demand function will favour consumers in higher income countries. Suppose the efficient market price in the Thai market is pT and the efficient market price in Germany is pG . The price set by *Econdork* will be some price pT < p∗ < pG . This means that the price will be above equilibrium price for Thai consumers reducing the total welfare in that market - Thai consumers would be willing to buy more units of the good at a lower price. On the other hand, the price will be below equilibrium price for German consumers. This unfairly gives consumers in higher income countries a greater consumer surplus and increased equilibrium quantity of goods. Thus the argument is valid on both efficiency and equity fronts. 2.2 Part b) If we ignore at first the prospect of in-game purchases, this is precisely 2nd degree price discrimination. Some individuals value the absence of advertisements very highly and as such setting a high price for removal of ads will allow the firm to cover the marginal cost for providing the game and thus can extract consumer surplus from this set of individuals. Another set of consumers may not value the absence of advertisements. As such, the firm can lower its marginal cost to zero by displaying paid advertisements and can efficiently charge nothing for the product while retaining profit from its income from advertisements. This line of thinking is a little nuanced since the consumers are not transferring some 8 of their surplus to the producer in the form of price discrimination but it does describe precisely the concept of ’self-sorting’: where consumers choose which product to purchase according to their preferences to transfer optimal producer surplus to *Econdork.* From another view: imagine the world where only the paid version is supplied: only the set of individuals who value the absence of advertisements enough in the game will purchase the good and because of the monopolistic power of *Econdork,* there will be a deadweight loss. By introducing another free product which is funded by advertisement revenue, the firm has been able to increase its revenue (overall producer surplus) while a) capturing a bigger share of the market and b) allowing both sets of users to access in-game purchases thus increasing opportunity for further revenue. 2.3 Part c) First, lets compute the total revenue and marginal revenue for Äppstore: T RÄ=20Q MR Ä= dQ Ä−Q Ä2 d(T R Ä) =20−2Q Ä Ä The firm will produce where the marginal revenue is equal to the marginal cost: M RÄ=M C Ä 20 − 2QÄ=2 QÄ∗ =9 PÄ∗ =11 ∗ πÄ = Q∗Ä · PÄ∗ − 2QÄ = 99 − 18 = 81 Now we have the case of a tariff which is applied in order to capture a greater part of consumer surplus. In fact, this question describes a special case of the two-part tariff which does not have any per-unit cost. Hence in this case, Spåttifaj will want to price their subscription such that they capture the entire consumer surplus when the price per unit is equal to their marginal cost. If they were to price per unit at their marginal cost (P = M C = 2), consumers would consume 18 songs and have a consumer surplus of 18·(20−2)/2 = 162. Hence if Spåttifaj were to charge a subscription price of 162, then consumers would still demand the subscription but would not have any consumer surplus. This would give a producer surplus (profit) of 162 − 18 · 2 = 126. 9 The problem with this analysis is that if the consumer purchases the subscription, **there is nothing to stop them downloading more songs since the marginal cost to the consumer is effectively zero.** Hence it is always logical to think that the consumer will download 20 songs (since this is their maximum demand) which increases the cost to the firm. A predatory firm could notice this and price the subscription assuming that at whatever price they set, the consumer surplus will be equal to the entire triangle under their demand curve. This gives a maximum willingness to pay for a subscription of 200 which gives a profit of 160. Which is now the final answer. 3 Q3 When companies merge or acquire other competitors, it is only permitted by Anti-Trust laws if it leads to synergies - this means that by combining resources, firms are able to cut costs, combine technologies and the end result is a better product at a lower price to the consumer. Thus the merger must be beneficial to the end-consumer. In the case of Facebook, the podcast argues that the company’s executives acquired Instagram and Whatsapp in order to suppress their competitive potential and thus increase the market power of Facebook. This would allow Facebook to charge higher markups for its advertisement product and thus increase the inefficiency in the social media advertisement market. One could additionally argue that this problem is exacerbated in the technology sector by incredibly low marginal costs resulting in increased super-normal profits and price setting abilities. An additional argument made is that it is damaging to users as Facebook 10 will obtain increased power to set its non-price setting rules such as privacy settings. With very little competition, users will have no choice but to accept. 11