1. Monopoly

2. Monopoly: Why? u Natural monopoly (increasing returns to scale), e.g. (parts of) utility companies? u Artificial monopoly –a patent; e.g. a new drug –sole ownership of a resource; e.g. a toll bridge –formation of a cartel; e.g. OPEC

3. Monopoly: Assumptions u Many buyers u Only one seller i.e. not a price-taker u (Homogeneous product) u Perfect information u Restricted entry (and possibly exit)

4. Monopoly: Features u The monopolist’s demand curve is the (downward sloping) market demand curve u The monopolist can alter the market price by adjusting its output level.

5. Monopoly: Market Behaviour y = Q p(y) Higher output y causes a lower market price, p(y). D

6. Monopoly: Market Behaviour What output level y* maximizes profit? Suppose that the monopolist seeks to maximize economic profit

7. Monopoly: Market Behaviour At the profit-maximizing output level, the slopes of the revenue and total cost curves are equal, i.e. MR(y*) = MC(y*)

8. Marginal Revenue: Example p = a – by (inverse demand curve) TR = py (total revenue) TR = ay - by 2 Therefore, MR(y) = a - 2by 0

9. Marginal Revenue: Example P = a - by a ya/b MR = a - 2by a/2b P MR= a - 2by < a - by = p for y > 0

10. Monopoly: Market Behaviour The aim is to maximise profits MC = MR < 0 MR lies inside/below the demand curve Note: Contrast with perfect competition (MR = P)

11. Monopoly: Equilibrium y = Q P MR Demand

12. Monopoly: Equilibrium y P MC MR Demand

13. Monopoly: Equilibrium y P AC MC MR Demand

14. Monopoly: Equilibrium y P AC MC MR Output Decision MC = MR ymym Demand

15. Monopoly: Equilibrium y P AC MC MR Demand P m = the price ymym PmPm

16. Monopoly: Equilibrium u Firm = Market u Short run equilibrium diagram = long run equilibrium diagram (apart from shape of cost curves) u At q m : p m > AC therefore you have excess (abnormal, supernormal) profits u Short run losses are also possible

17. Monopoly: Equilibrium y P AC MC MR Demand The shaded area is the excess profit ymym PmPm

18. Monopoly: Elasticity WHY? Increasing output by  y will have two effects on profits 1)When the monopoly sells more output, its revenue increase by p  y 2)The monopolist receives a lower price for all of its output

19. Monopoly: Elasticity Rearranging we get the change in revenue when output changes i.e. MR

20. Monopoly: Elasticity  = elasticity of demand

21. Monopoly: Elasticity Recall MR = MC, therefore, Therefore, in the case of monopoly,  < -1, i.e. |  |  1. The monopolist produces on the elastic part of the demand curve.

22. Application: Tax Incidence in Monopoly y P MC MR Demand MC curve is assumed to be constant (for ease of analysis)

23. Application: Tax Incidence in Monopoly u Claim When you have a linear demand curve, a constant marginal cost curve and a tax is introduced, price to consumers increases by “only” 50% of the tax, i.e. “only” 50% of the tax is passed on to consumers

24. Application: Tax Incidence in Monopoly y P MC bt MR Demand y bt Output decision is as before, i.e. MC=MR So Y bt is the output before the tax is imposed

25. Application: Tax Incidence in Monopoly y P MC bt MR Demand y bt Price is also the same as before P b t = price before tax is introduced. P bt

26. Application: Tax Incidence in Monopoly y P MC bt MR Demand y bt The tax causes the MC curve to shift upwards MC at P bt

27. Application: Tax Incidence in Monopoly y P MC bt MR Demand y bt The tax will cause the MC curve to shift upwards. MC at P bt

28. Application: Tax Incidence in Monopoly y P MC bt MR Demand y bt Price post tax is at P pt and it higher than before. MC at P bt y at P pt

29. Application: Tax Incidence in Monopoly Formal Proof Step 1: Define the linear (inverse) demand curve Step 2: Assume marginal costs are constant MC = C Step 3: Profit is equal to total revenue minus total cost

30. Application: Tax Incidence in Monopoly Formal Proof Step 4: Rewrite the profit equation as Step 5 : Replace price with P=a-bY Profit is now a function of output only

31. Application: Tax Incidence in Monopoly Formal Proof Step 6: Simplify Step 7: Maximise profits by differentiating profit with respect to output and setting equal to zero

32. Application: Tax Incidence in Monopoly Formal Proof Step 8: Solve for the profit maximising level of output (Y bt )

33. Application: Tax Incidence in Monopoly Formal Proof Step 9: Solve for the price (P bt ) by substituting Y bt into the (inverse) demand function Recall that P = a - bY therefore

34. Application: Tax Incidence in Monopoly Formal Proof Step 10: Simplify Multiply by - b b cancels out

35. Application: Tax Incidence in Monopoly Formal Proof

36. Step 11: Replace C = MC with C = MC + t (one could repeat all of the above algebra if unconvinced) So price after the tax P at increases by t/2 Price before tax