Unit 4 (Monopolies) PDF

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Unit 4 (Monopolies)...

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Monopolies - Competition case:! - Firms maximise profit! - FOC: MR=MC! - MR = p’y+p! - No entry barriers —> if there is profit, new companies enter! - Infinite number of companies, each so small that they’re price takers (p’=0) and MR=p! - Companies maximise profit when MC=p! - Monopoly case:! - Quantity sold affects the price! - Method to calculate optimal q and p is the same! - MR=MC (MR=p’y+p and p’≠0)! - Firm will move from A to B only if the increase in price is stronger than the quantity decrease (in other words P*Q total increases)! - OR: max π = p(y)y-c(y)!

- Assumptions:! - p’(x)40! - Maximum price equal to competitive equilibrium price:! - For maximum price pm=p*=45 and produce 45 units! - Maximum price below competitive equilibrium price:! - For maximum price pm=40 only 40 units produce! - These is scarcity! - Natural monopolies - Example: p(x)=10-x; c(x)=16+x2/2 x>0! - Monopolist solution: 10-2x=x —> Xm=10/3 and pm=20/3! - We need to check if π>0; π=p(x)*x-c(x) =20/3*10/3-16-(10/3)2/2 = 2/3! - 2/3>0, market active! - Could cost efficient solution be provided?! - MC=p! - 10-x=x —> x=5! - π=-3.5 therefore market wouldn’t be active, MR=MC better solution! - To keep market active we must set P=6!

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Price discrimination - We have assumed that monopolist sells for the same price to everyone, but it may be the case that this doesn’t occur! - Definition: selling the same product to different persons for different prices! - In some cases, discrimination can be desirable! - 3 cases:! - First degree: individual prices for each consumer! - Second degree: discrimination via quality or quantity (self-selection)! - Third degree: discrimination by groups based on observable characteristics! Third degree explained - Maximisation problem is:!

- Example:! - p1(x1) = 10 - x1 ! - p2(x2) = 6! - c(x)=x2/2! - First calculate aggregate demand and solve as usual:!

! First degree discrimination - First degree is like third degree, but taken to the extreme, every agent is an individual “market”! - In this case, company will offer products at a price = to the consumer’s reservation price! - Hence, the company will extract all consumer surplus.! - If we want to extend it to multiple units, firm offers a take-it-or-leave-it option:! - Under quasi-linear preferences, monopolist will set Ai such that Ai=v(qi)! - Monopolist will continue offering until v’(qi)=MC(j)! - Again, the monopoly will extract all consumer surplus! - Graphically, we can see how the monopoly sets p*=reservation price&

Second-degree price discrimination - Monopolist’s know there are different groups of consumers, but cannot tell them apart, these groups differ by preferences for quality/quantity! - Quantity: beers in a bar or frequency in metro! - Quality: economy/business/first class and different smartphones! - Monopolies can’t treat consumers differently, but they can design different bundle sets to induce different behaviours.! - “Self selection” of consumers based on their preferences! - Assume two types of consumers H and L! - H prefers higher quality, so willingness to pay for any quantity of the good is higher than of L! - Assume that the monopolist is only allowed to offer a menu of choices (q,A)! - Consumers can freely choose from menu or not buy anything (0,0), is always an option! Example:! - Two consumers H and L! - Marginal utilities:! - H: V’H(q)= 10-q! - L: V’L(q)= 8-q! - Cost: c(x)=0! - Intuitively, since there are only two consumers, we need at most two bundles:! - Bundle (qH,AH) targeted at H! - Bundle (qL,AL) targeted at L! - If monopolist knows the type of consumers and can discriminate, then optimal solution will be:! - Ds! - Problem: consumers are free to choose the bundle from the menu therefore consumer H won’t chose their given bundle as they can get a positive surplus by buying bundle L, 8 x 2 = 16!

- To ensure H chooses bundle H, we need to reduce AH such that H’s surplus is at least as high, in this case, since surplus is 16, AH = 50 -16 = 34!

- Total profit is 66, which 66>64! - We treat consumers equally, but self-selection leads to higher profit than by using a one-item menu!

- Changing quantity of H (more expensive bundle) - If we reduce qH we also need to reduce AH! - Also, this would only affect agents H, as this bundle is too expensive for L! - If we reduce qH enough to make it attractive for L, then one-item menu best-case scenario (nothing is gained)!

- Changing quantity of L (cheaper bundle) - If we reduce qL there are two effect:! - We have to reduce AL (standard)! - We can increase AH (alternative L now less attractive)!

- Let’s look at the implications in our example:! - Reducing qL from 8 to 7:!

- AL=31.5, but H “looses” 2 units of surplus from bundle L; we can set AH=36, so that π=67.5! - If we continue to distort qL up to =6 then π=68.! Formal solution - Assumptions:! - UH=vH(qH)+mH! - UL=vL(qL)+mL! - In the relevant region:! - VL(0)=VH(0)=0! - V’≥0 and V’’...