The marginal cost of producing a beer is constant at 4, meaning that the supply curve for beer is a horizontal line at P=4. After a long day of work, you feel like your first beer of the evening is worth 10. Each subsequent beer loses about 2 of value (i.e., 8 for the second, 6 for the third…). How many beers do you buy? And what is your total consumer surplus?

Question

BlackTom AI · Accepted Answer

We start by restating the key setup and what it implies for buying decisions.
- The marginal cost of producing a beer is constant at 4, so the market supply curve is a horizontal line at P = 4.
- The consumer’s willingness to pay (WTP) for successive beers declines: 10 for the first, 8 for the second, 6 for the third, 4 for the fourth, 2 for the fifth, and so on.

Next, we determine how many beers the consumer buys by comparing each beer's WTP to the price (which is 4 in this market):
- Beer 1: WTP = 10, price = 4. The consumer purchases it because 10 > 4, yielding a per-beer surplus of 10 − 4 = 6.
- Beer 2: WTP = 8, price = 4. Purchase occurs since 8 > 4, yielding surplus 8 − 4 = 4.
- Beer 3: WTP = 6, price = 4. Purchase occurs since 6 > 4, yielding surplus 6 − 4 = 2.
- Beer 4: WTP = 4, price = 4. Purchase occurs at the threshold since 4 = 4, yielding surplus 4 − 4 = 0.
- Beer 5: WTP = 2, price = 4. Do not purchase because 2 < 4.

Now, let’s sum up the consumer surplus from each beer actually purchased:
- Surplus from beer 1: 6
- Surplus from beer 2: 4
- Surplus from beer 3: 2
- Surplus from beer 4: 0
Total CS = 6 + 4 + 2 + 0 = 12.

A few scenarios to check for potential confusion:
- If the price were above 4, the fourth beer wouldn’t be bought, reducing CS and quantity accordingly.
- If the price were below 4, the fifth beer might be purchased, but then the CS would change due to the lower price, and the WTP sequence would still cap purchases when WTP falls below price.
- The fact that the marginal cost is constant and equals the market price means each additional beer bought adds zero or positive surplus depending on the gap between WTP and price, as seen in the first three beers and the fourth ending at zero.

In summary, the consumer buys beers as long as their willingness to pay exceeds or equals the market price, and the total consumer surplus is the sum of the differences between WTP and price for those beers. Here, four beers are purchased with a combined surplus of 12, while the fifth beer is not purchased because its WTP drops below the price.

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