# Monopoly Monopoly Why u Natural monopoly increasing returns

- Slides: 36

Monopoly

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

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)

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.

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

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

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*)

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

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

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)

Monopoly: Equilibrium P MR Demand y=Q

Monopoly: Equilibrium MC P MR Demand y

Monopoly: Equilibrium MC P AC MR Demand y

Monopoly: Equilibrium MC P Output Decision AC ym MR Demand MC = MR y

Monopoly: Equilibrium MC P Pm = the price AC Pm ym MR Demand y

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

Monopoly: Equilibrium MC P AC Pm ym MR The shaded area is the excess profit Demand y

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

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

Monopoly: Elasticity = elasticity of demand

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.

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

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

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

Application: Tax Incidence in Monopoly Price is also the same as before P Pbt = price before tax is introduced. Pbt MCbt ybt MR Demand y

Application: Tax Incidence in Monopoly The tax causes the MC curve to shift upwards P Pbt MCat MCbt ybt MR Demand y

Application: Tax Incidence in Monopoly The tax will cause the MC curve to shift upwards. P Pbt MCat MCbt ybt MR Demand y

Application: Tax Incidence in Monopoly Price post tax is at Ppt and it higher than before. P Ppt Pbt MCat MCbt yat ybt MR Demand y

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

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

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

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

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

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

Application: Tax Incidence in Monopoly Formal Proof

Application: Tax Incidence in Monopoly Formal Proof Step 11: Replace C = MC with C = MC + t (one could repeat all of the above algebra if unconvinced) Price before tax So price after the tax Pat increases by t/2

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