Term 1 Lecture 3 Flashcards
(35 cards)
Monopoly model setup
Profit = Revenue - Costs
= q.P(q) - C(q,w) , where w are input prices and q is output
- to maximise profit, we differentiate and set the slope of profit = 0, so MR = MC
MR does not equal price, why
MR = q.DP/Dq + P(q) < P(q), as to sell more the monopolise has to cut price on all units it sells not just the additional unit
- downward sloping demand curve, so DP/Dq < 0
Monopoly pricing rule: Lerner Index and Elasticity
P(q) = MC/(1+1/PED)
- derived using the profit max conditon
- equation tells us that as MC rises, monopolist raises prices
- as demand becomes more elastic, price falls
(P - MC) / P = -1/PED, measures the firms price markup over MC as a proportion of price, so if demand is elastic, markup power is low
- closer to 1 means greater monopoly power.
Two part tariffs
Price paid by consumer for buying Q units is A + PQ, where A is a fixed fee, and p is the price for units
- average price declines in Q - almost a quantity discount
Total revenue in two part tariff case:
- what’s the profit max condition then?
TR = integrate p(v), limits q and 0
MR = D/Dq (TR) = p(q)
MC = MR therefore means:
P(q) = MC, same way a perfectly competitive firm would set prices
How to set A in a two part tariff?
So at a price, consumer will demand x amount. But by doing this, they are naturally gaining a consumer surplus of some amount.
So set a fixed fee equal to this consumer surplus, and they will still buy
Necessary conditions for price discrimination
- market segmentation - possible to identify at least 2 market segments with different PED
- preventing resale - price discrimination can only work if consumers paying lower price can’t easily resell the product to those who would pay more
1st degree price discrimination
A firm charges a customised price for each individual based on their willingness to pay
- in theory captures all consumer surplus
- revenue would equal area under the demand curve
2nd degree price discrimination
- occurs when a firm charges different prices based on quantity purchased
3rd degree price discrimination
Firm divides consumers into 2+ broad market segments and charges different prices to each based on PED
- sets prices based on PED in each market segment, using the monopoly pricing rule
Regulation of monopoly
Most common form of regulation is price cap
- MR curve changes, as long as price is lower than max price, MR becomes flat and equal to the regulated price
- once Pmax hits AR, firm’s MR returns to its original curve
Monopsonies
Buyer has market power over sellers, allows monopsonist to set wages and control the quantity purchased of labour in this case
- they know more labour they hire, higher wages to pay, so monopsonist hires less labour than would be in a perfectly competitive labour market to keep wages low
Monopsonist labour market model
Profit = PL^0.5 - wL supply L=2w
In perfect competition
In perfect comp, maximise keeping w fixed:
= L = (p/2w)^2, this demand curve gives
- w* = 0.5p^2/3, L* = p^2/3
Monopsonist labour market model
Profit = PL^0.5 - wL
In monopsonist market
L = 2w
Profit = pL^0.5 - (0.5L).L
- MRP = ME, monopsonist wants to stop buying labour when extra revenue gained is = to extra expenditure on labour
- (0.5p)/(L^-0/5) = L
L* = (0.5p)^2/3, w* = ((0.5)^2/3)/2), a lower wage and quantity of labour than perfect competiton
Bilateral monopoly
One buyer and one seller
- outcome determined by bargaining power of each party
Bilateral monopoly in perfect competition
Seller produces until MC = P
- P = c’(x)
Buyer consumes unit MU = P
- P = u’(x), satisfies MC = MU, a Pareto efficient outcome
Bilateral monopoly in a monopoly
Seller has bargaining power, so moves first and sets prices p, profit maximising s.t. P = u’(x)
- buyer will purchase x units such that p = u’(x)
- definitely not Pareto efficient, very good for the seller.
Bilateral monopoly outcome in a monopsony
Buyer has a lot of bargaining power, so they move first and set the price, seller then decides how much to produce at that price
- maximises utility subject to p = c’(x) and then seller gets profits based on those outcomes
Bilateral monopoly in a bargaining/negotiation situation
- 1st step is determining the possible outcomes and what each party can get if they agree or fail to agree
- if they dont agree, assume utility of 0 as no trade and no competition
- any agreement must be Pareto efficient, so no one can be made better off without making the other worse off
- so u’(x) = c’(x)
- set of possible agreements is a triangle in the buyer-seller utility space, exact outcome depends on bargaining power.
Bilateral monopoly with a Nash bargainin setup
Max (u(x) - F)^a.(F - c(x))^(1-a)
- where a represents the bargaining power of the buyer
F = ac(x) + (1-a)u(x), a weighted average of the buyer’s utility and the seller’s cost, with weighs determined by bargaining power a
- of a is 1, buyer captures all the curious and vice
- equation also shows the Pareto frontier is linear
Cournot’s model of oligopoly
- firms compete by choosing the quantity of output to produce
- each firm produces a homogenous product
- price in the market is determined by the total output produced by both
How to find best responses in cournot oligopoly
- Maximise the profit function for firm 1 with respect to Q1
- Or, find firm 1s revenue, find MR and set to MC
3 points worth emphasising for the BRFs in cournot
- Slope down usually, as competition produces more, less demand for me, so optimal to produce less
- Intercepts are informative, as if q2 = 0, firm 1 is alone, so it is the output of a monopolist
- When Q2 is very high, firm 1 wants to produce 0 output as it makes 0 profit, 0 profit, zero profit is a characteristic of perfect comp
Finding the cournot/nash equilibrum
Set the BRFs equal to each other and solve
Only works when firms have same costs and demands
