Monopoly Monopoly: Why? Natural monopoly (increasing returns to scale), e.g . (p arts of) utility companies? 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 Many buyers Only one seller i.e . not a price-taker (Homogeneous product) Perfect information Restricted entry (and possibly exit) Monopoly: Features The monopolist’s demand curve is the (downward sloping) market demand curve The monopolist can alter the market price by adjusting its output level. Monopo ly: Marke t Be hav iou r 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 ( y) p( y) y c( y) TR TC 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 - by2 Therefore, MR(y) = a - 2by < a - by = p for y > 0 Marginal Revenue: Example MR= a - 2by < a - by = p P for y > 0 P=aP = a - by a a/2b a/b y MR = a - 2by Monopoly: Market Behaviour The aim is to maximise profits MC = MR p MR p y p y < 0 MR lies inside/below the demand curve Note: Contrast with perfect competition (MR = P) Monopo l y: Equ ilib riu m P MR Demand y=Qy = Q Monopo l y: Equ ilib riu m MC P MR Demand y Monopo l y: Equ ilib riu m MC P AC MR Demand y Monopo l y: Equ ilib riu m MC Output Decision P AC MC = MR y m MR Demand y Monopo l y: Equ ilib riu m MC Pm = the price P AC Pm y m MR Demand y Monopoly: Equilibrium Firm = Market Short run equilibrium diagram = long run equilibrium diagram (apart from shape of cost curves) At qm: pm > AC therefore you have excess (abnormal , supernormal) profits Short run losses are also possible Monopo l y: Equ ilib riu m MC The shaded P AC area is the excess Pm profit y m MR Demand y Monopolyyy: Elasticity TR py yp WHY? Increasing output by y will have two effects on profits 1) When the monopoly sells more output, its revenue increase by py 2) The monopolist receives a lower price for all of itsoutttput Monopolyyy: Elasticity TR py yp Rearranging we get the change in revenue when output changes i.e. MR TR p MR p y y y TR y p MR p 1 y p y Monopo l y: Elas tic ity TR y p MR p 1 y p y 1 = elasticity of demand TR 1 MR p 1 y Monoppyoly: Elasticit y Recall MR = MC, therefore, R 1 MR p1 MC0 y Therefore, in the case of monopoly, < -1ie1, i.e. || 1. The monopolist produces on the elastic part of the demand curve. Application: Tax Incidence in Mono pol y P MC curve is assumed to be constant (for ease of analysis) MC MR Demand y Application: Tax Incidence in Monopoly Claim When you have a linear demand curve, a constant marginal cost curve andiiddid a tax is introduced, price to consumers increases byyy “only” 50% of the tax, i.e. “only” 50% of the tax is passed on to consumers Application: Tax Incidence in Mono pol y Output decision is as before, i.e. P MC=MR So Ybt is the output before the tax is imposed MCbt y bt MR Demand y Application: Tax Incidence in Mono pol y Price is also the same as before P Pbt = price before tax iitdis introduced . Pbt MCbt y bt MR Demand y Application: Tax Incidence in Mono pol y The tax causes the MC curve to shift P upwards Pbt MCat MCbt y bt MR Demand y Application: Tax Incidence in Mono pol y The tax will cause the MC curve to shift upwards. P Pbt MCat MCbt y bt MR Demand y Application: Tax Incidence in Mono pol y PiPrice post tt tax i s at tP Ppt P and it higher than bfbefore. Ppt Pbt MCat MCbt y yat bt MR Demand y Application: Tax Incidence in Monopoly Formal Proof Step 1 : D efi ne th e li near (i nverse) d emand curve P a bY Step 2: Assume marginal costs are constant MC = C Step 3: Profit is equal to total revenue minus total cost TR TC Application: Tax Incidence in Monopoly Formal Proof Step 4: Rewrite the profit equation as PY CY Step 5 : Replace price with P=a-bY a bY Y CY Profit is now a function of output only Application: Tax Incidence in Monopoly Formal Proof Step 6: Simplify Ya bY 2 CY Step 7: Maximise profits by differentiating ppppgrofit with respect to output and setting equal to zero ' a 2bY C 0 Y Application: Tax Incidence in Monopoly Formal Proof Step 8: Solve for the profit maximising level of output (Ybt) 2bY C a a C Y bt 2b Application: Tax Incidence in Monopoly Formal Proof Step 9: Solve for the price (Pbt) by substituting Ybt into the (inverse) demand function a C Y bt 2b Recall that P = a - bY therefore a C Pbt a b 2b Application: Tax Incidence in Monopoly Formal Proof Step 10: Simplify a C Pbt a b 2b ba bC Multiply by Pbt a 2b -b a C Pbt a b cancels 2 out Application: Tax Incidence in Monopoly Formal Proof a C Pbt a 2 2 1 C Pbt a a 2 2 1 C a C P a P bt 2 2 bt 2 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) a C P Price before tax bt 2 a C t So price after the Pat tPtax Pat ibincreases by 2 t/2.