While working for Madison Mayer’s Office you were investigating the local farmers’ markets and came up with the following table for the tomato market:

Price $

Demand

Supply

10

20

5

20

10

10

Using the information in the table above, what is the equation of the supply curve for tomatoes (assume it is linear)?

Answer:
[ Select ]
Qs = 0.5P
Qs = 10 + 0.5P
Qs = 2P
Qs = 7.5 + 0.5P
Qs = 10 + 2P

Question

While working for Madison Mayer’s Office you were investigating the local farmers’ markets and came up with the following table for the tomato market:

Price $

Demand

Supply

10

20

5

20

10

Using the information in the table above, what is the equation of the supply curve for tomatoes (assume it is linear)?

Answer: 
[ Select ]
Qs = 0.5P
Qs = 10 + 0.5P
Qs = 2P
Qs = 7.5 + 0.5P
Qs = 10 + 2P

BlackTom AI · Accepted Answer

Supply is positively related to price, so the linear supply curve can be written as Qs = a + bP (with b > 0). Use the two supply observations to solve for a and b.

1) Relevant knowledge points and concepts
- A linear supply function has the form Qs = a + bP, where a is the intercept and b is the slope (change in quantity supplied per unit change in price).
- Use the given price–supply pairs to determine a and b.

2) Complete reasoning process step by step
- From the table the supply observations are:
  - When P = 10, Qs = 5
  - When P = 20, Qs = 10
- Substitute these into Qs = a + bP to get two equations:
  (1) 5 = a + b(10)
  (2) 10 = a + b(20)

3) Calculations with intermediate steps
- Subtract (1) from (2): 10 − 5 = [a + 20b] − [a + 10b] → 5 = 10b → b = 5/10 = 0.5
- Substitute b = 0.5 into (1): 5 = a + 0.5(10) → 5 = a + 5 → a = 0

- Therefore Qs = 0 + 0.5P → Qs = 0.5P

4) Why the correct answer is correct
- Qs = 0.5P exactly reproduces both observed points: at P = 10, Qs = 0.5·10 = 5; at P = 20, Qs = 0.5·20 = 10. The slope is positive (supply rises with price) and the intercept is zero given the data.

5) Why other options are incorrect
- Qs = 10 + 0.5P gives Qs = 15 at P = 10 (not 5).
- Qs = 2P gives Qs = 20 at P = 10 (not 5).
- Qs = 7.5 + 0.5P gives Qs = 12.5 at P = 10 (not 5).
- Qs = 10 + 2P gives Qs = 30 at P = 10 (not 5).
None of these reproduce the observed supply values.

6) Conclusion
The derived linear supply curve is Qs = 0.5P, which matches the provided correct answer.

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