Selling more cups is not the goal. Selling every cup that adds more than it costs, and no others, is. This week you find the line between them.
Learning objectives. After this week you can (1) compute marginal revenue; (2) apply the MR = MC rule; and (3) use the shutdown rule to compare opening with staying dark.
Remember this: a cup is worth selling when it adds more revenue than cost.
1) Marginal revenue and the MR = MC rule
Marginal Revenue = change in Total Revenue ÷ change in Quantity
Profit is maximized where Marginal Revenue = Marginal Cost
Revenue rises from $100 to $120 when one more unit sells: MR = $20. A price taker sells every unit at the market price, so its MR equals the price. Selling at $10:
| Unit | Marginal revenue | Marginal cost | Effect on profit |
|---|---|---|---|
| 1st | $10 | $6 | Adds $4 |
| 2nd | $10 | $7 | Adds $3 |
| 3rd | $10 | $10 | MR = MC: profit peaks here |
| 4th | $10 | $13 | Loses $3 |
If MR > MC, the next unit adds profit. If MC > MR, it subtracts. Producing past MR = MC shrinks profit.
2) MR when you set your own price
Your shop is not a price taker: to sell more cups you charge less, so MR sits below price. Your report has both numbers you need:
MR = Price × (1 + 1 ÷ ε)
Latte $5.00 and ε −2.0: MR = $5.00 × (1 + 1 ÷ −2.0) = $5.00 × 0.5 = $2.50. If your MC latte line reads $1.20, the next latte adds about $1.30 more than it costs. If MR came out below MC, your last lattes would be costing more than they bring in.
3) The shutdown rule
Shut down in the short run if Price < Average Variable Cost
Fixed costs are owed whether you open or not, so they don't decide the question. Compare what opening brings in with what a dark day avoids: wages, COGS and spend. Say Revenue is $900 against $480 of wages, $230 of COGS and $90 of spend ($800 in all), with Fixed of $250. Net today is −$150, but a dark day would have lost the whole $250, so opening was the smaller loss. At exactly AVC, opening and closing lose the same. Your report's AVC line counts ingredients only, so add wages and spend yourself for this test.
Quick self-check
(a) At $10 per unit, MC is $6, $7, $10, then $13. Which quantity maximizes profit? (b) Latte $4.00 and ε −4.0. What is MR? (Answers: 3 units, where MR = MC = $10; $4.00 × 0.75 = $3.00.)
Common mistakes
- Using ATC for the shutdown decision. Fixed costs are paid either way.
- Treating MR as the price. When you set your own price, MR is lower.
- Losing the sign of ε. 1 + 1 ÷ (−2.0) is 0.5, not 1.5.
This week in the arena
Take one Daily Report. Compute your MR from your latte price and the report's ε, then set it next to the MC latte line. Which is bigger, and by how much? If you had a losing day, check it too: did Revenue cover Wages, COGS and Spend?