Profit Maximization

Profit Maximization assuming: Firm must charge every consumer the same price (i.e., no price discrimination) No Strategic Interaction among Firms We will consider three industry structures: Price taking Firms Monopoly Monopolistic Competition

Price Taking Firm’s Short Run Costs Q FC VC TC AFC AVC ATC MC 100 -   50 1 150 30 2 80 180 40 90 20 3 200 33.3 33.33 66.7 10 4 110 210 25 27.5 52.5 5 130 230 26 46

Price Taking Firm’s Short Run Costs Q FC VC TC AFC AVC ATC MC 5 100 130 230 20 26 46   30 6 160 260 16.7 26.67 43.3 40 7 200 300 14.3 28.57 42.9 50 8 250 350 12.5 31.25 43.8 60 9 310 410 11.1 34.44 45.6 70 10 380 480 38 48

What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits? 8 55*8-43.75*8=90

What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits? 6 35*6-43.33*6=-50 Produce an output of 6 in short-run if fixed costs are sunk.

What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits? 5? 25*5-46*5=-105 Better off producing 0 so profits=-FC=-100

Short-Run Profit Maximizing Rule Produce at an Output where Marginal Revenue = Marginal Cost (MR) (MC) if Total Revenue > Variable Cost [When the firm cannot price discriminate, this is the same thing as saying as long as Price > AVC (from P*Q > AVC*Q) ]

Monopoly Characteristics There is a single seller There are no close substitutes for the good There are extremely high barriers to entry

Natural Monopoly (type of monopoly where there exists large economies of scale) $/unit when a single firm can supply a good or service to an entire market at a smaller cost than could two or more firms. Long Run Average Total Cost ATC1/2 big firm ATCone big firm Q1/2 big firm Qbig firm Quantity 60

Monopolist Marginal Revenue (with no price discrimination) Q TR MR 10 9 1 8 2 16 7 3 21 6 4 24 5 25 +9 +7 +5 +3 +1 -1 Q -3 -5 MR -7 Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit. -9

Use Calculus to Obtain MR curve for Linear Demand Curve P=a-bQ Slope of D TR = (a-bQ)Q =aQ-bQ2 MR =ΔTR/ ΔQ =∂TR/ ∂Q =a-2bQ [In prior graph, a=10 and b=1] Slope of MR

Monopoly Elastic Inelastic If the firm’s goal were to maximize total revenue, where would it produce? P=$5; hD=-1; TR=$25 Inelastic The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR? Elastic: MR>0 Inelastic: MR<0 Q Will a monopolist ever produce on the inelastic portion of the demand curve? No. MR

Monopoly Maximizing Profits If the monopolist maximizes profits, where would it produce? At an output where MR=MC as long as P>AVC. This is at an output of Q=4 so a price of P=6. Q MR

MATH BEHIND: Maximizing Profits being where MR=MC MaxQ Profits = MaxQ TR(Q)-TC(Q) so profits are maximized where Or where, Applies when Q>0

Monopoly Maximizing Profits At Q=4 and P=6, what is Total Revenue? TR=P*Q=6*4=24 At Q=4, what are Total Costs? TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what are Profits? Profits=TR-TC=24-18=6 Or Profits=P*Q-ATC*Q =(P-ATC)*Q =(6-4.5)*4=6 TR Profits Q TC MR

Monopolist in Long Run What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand? Keep producing Q=4 or change plant size depending if there is a plant size that would result in greater profits. Profits Q MR

Short Run and Long Run ATCs

Monopolist in Long Run Profits What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand? Exit the industry or change plant size depending if there is a plant size that would result in positive profits given demand curve. MR

Monopolistic Competition Characteristics There are many buyers and seller Each firm in the industry produces a differentiated product There is free entry into and exit from the industry [Think bakery or coffee shop in big city.]

Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Short Run If bakery maximizes profits, where would it produce? Where MR=MC which is at an output of Q=3.5 so a price of P=8. What are the bakery’s profits? TR-TC=P*Q-ATC*Q =8*3.5 - 6.25*3.5 = 6.12 MR

Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Long Run In long-run if the bakery is making positive economic profits, we would expect other bakeries to enter causing a reduction in demand. What are maximum profits when demand is D’? Q=3 so a price of P=6.67. Profits=P*Q-ATC*Q =6.67*3-6.67*3=0 D’ MR

Review of Profit Maximization (when setting a single price)

Marginal Revenue from 5th Unit is just the shaded area below Marginal Revenue from 5th Unit is just the shaded area below. This area is $11. When the MR curve is linear, the area under the MR curve can be obtained by just taking the MR at the midpoint of the quantities – in this case at 4.5. The orange area is the same as the purple area. MR

Marginal Cost of 5th Unit is just the shaded area below Marginal Cost of 5th Unit is just the shaded area below. This area is $9. When the MC curve is linear, the area under the MC curve can be obtained by taking the MC at the midpoint of the quantities – in this case at 4.5. The purple area is the same as the red area MR

Change in Profits associated with producing 5 Units rather than 4 units. Yellow area is change in profits associated with producing 5 units rather than 4 units. This area is $2. Subtract MC of 5th unit from MR of 5th unit– brown area from purple. MR

Review of Profit Maximization (when setting a single price)

PROFIT MAXIMIZATION Profits are maximized at an output where MR=MC which is Q=5. Price is 15 and ATC is 11.2 at Q=5. Profits are then 15*5-11.2*5=19 15 11.2 MR