Market Structures, Costs and Revenue: Question 3

Worked solution

Part (a): Total revenue and marginal revenue

Total revenue $TR = P \times Q$ at each output:

$TR(1)=100\times1=100,\quad TR(2)=90\times2=180,\quad TR(3)=80\times3=240$ $TR(4)=70\times4=280,\quad TR(5)=60\times5=300,\quad TR(6)=50\times6=300$

Marginal revenue is the change in total revenue from selling one more licence (taking TR at zero output as $0):

$MR(1)=100-0=100,\quad MR(2)=180-100=80,\quad MR(3)=240-180=60$ $MR(4)=280-240=40,\quad MR(5)=300-280=20,\quad MR(6)=300-300=0$

Part (b): Marginal cost

With fixed cost of $50 at zero output, marginal cost is the change in total cost from producing one more licence:

$MC(1)=70-50=20,\quad MC(2)=100-70=30,\quad MC(3)=135-100=35$ $MC(4)=175-135=40,\quad MC(5)=245-175=70,\quad MC(6)=355-245=110$

Part (c): Profit-maximising output and profit

Comparing the MR and MC rows:

MR exceeds MC at outputs 1, 2 and 3 (each extra licence adds more to revenue than to cost, so producing it raises profit), while MC exceeds MR at outputs 5 and 6 (each extra licence there would add more to cost than to revenue). Exactly at $Q=4$, $MC=MR$ at $40: the 4th licence adds precisely as much to revenue as it costs to supply, so producing it leaves total profit unchanged. Applying the profit-maximising rule ($MC=MR$), EconoSoft’s profit-maximising output is 4 licences per month.

Profit at this output is total revenue minus total cost:

$\text{Profit}(4) = TR(4) - TC(4) = 280 - 175 = 105$

This is a profit of $105.

(Since the 4th licence’s $MR$ exactly equalled its $MC$, it added nothing extra to profit, profit at 3 licences is also $105, but the standard $MC=MR$ rule identifies 4 licences as the profit-maximising output, since output can be expanded up to this point without any loss of profit.)

Part (d): Why AR exceeds MR for EconoSoft, but AR equals MR in perfect competition

EconoSoft is the only supplier of this app, so it faces the entire market demand curve, which slopes downward. To sell one more licence, it must lower the price on all the licences it sells, not only the extra one, so the revenue gained from the extra licence is reduced by the lost revenue from charging a lower price on every unit it was already selling. This is exactly why marginal revenue is below price (average revenue) at every output beyond the first unit.

A firm in perfect competition, by contrast, supplies such a small share of a market containing many identical sellers that it can sell as much as it wishes at the going market price without needing to lower that price at all. Its demand curve is therefore horizontal (perfectly elastic) at the market price, so each extra unit sold adds exactly the market price to revenue. Meaning average revenue equals marginal revenue equals price at every output.

Final answers

• (a) TR $=$ 100, 180, 240, 280, 300, 300; MR $=$ 100, 80, 60, 40, 20, 0 (for Q $=$ 1–6)
• (b) MC $=$ 20, 30, 35, 40, 70, 110 (for Q $=$ 1–6)
• (c) Profit-maximising output $=$ 4 licences per month (where MC $=$ MR $=$ $40); profit $=$ $105
• (d) EconoSoft must cut price on all units to sell more, so MR $<$ AR; a perfectly competitive firm sells at a fixed market price, so AR $=$ MR