After many weeks working at Madison Mayer’s Office you construct the following table that includes two points on the Production Possibilities Frontier (PPF). You simplified Madison’s economy and assumed that Madison produces only cheese and beer.

Cheese

Beer

Pair 1

1,500

0

Pair 2

0

3,000

Assume that the PPF is straight line. What is the opportunity cost of beer in terms of cheese? Answer:1/2

Question

After many weeks working at Madison Mayer’s Office you construct the following table that includes two points on the Production Possibilities Frontier (PPF). You simplified Madison’s economy and assumed that Madison produces only cheese and beer.

Cheese

Beer

Pair 1

1,500

0

Pair 2

0

3,000

Assume that the PPF is straight line.  What is the opportunity cost of beer in terms of cheese? Answer:1/2

BlackTom AI · Accepted Answer

Opportunity cost of one beer equals how much cheese must be given up to produce that beer.

1) Relevant concepts:
- The Production Possibilities Frontier (PPF) shows trade-offs between two goods. 
- A straight-line PPF implies a constant opportunity cost. 
- The slope of the PPF (change in cheese divided by change in beer) gives the cheese forgone per additional beer (with a negative sign indicating the trade-off).

2) Step-by-step reasoning and calculations:
- Two points on the PPF: (Cheese, Beer) = (1500, 0) and (0, 3000).
- Compute the slope: slope = (change in cheese) / (change in beer).
- change in cheese = 0 − 1500 = −1500.
- change in beer = 3000 − 0 = 3000.
- slope = −1500 / 3000 = −1/2.
- The negative sign indicates that cheese falls when beer rises. The absolute value (1/2) is the opportunity cost of one additional beer measured in cheese.

3) Intermediate steps shown:
- slope = (0 − 1500) / (3000 − 0) = −1500 / 3000 = −0.5.
- |slope| = 0.5 cheese per beer = 1/2 cheese per beer.

4) Why this is correct:
- Starting at the cheese-focused point (1500 cheese, 0 beer) and moving to the beer-focused point (0 cheese, 3000 beer) sacrifices 1500 cheese to gain 3000 beer. Dividing cheese forgone by beers gained gives cheese per beer = 1500/3000 = 1/2. Since the PPF is linear, this rate holds for each additional beer.

5) Other possible answers and why they are incorrect:
- Any value other than 1/2 (for example 2 cheese per beer or 1 cheese per beer) contradicts the computed ratio 1500/3000. The reciprocal (2 beers per cheese) is the opportunity cost of cheese measured in beer, not of beer measured in cheese.

Conclusion: The opportunity cost of beer in terms of cheese is 1/2, matching the provided answer.

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