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: Qs = 0.5P

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: Qs = 0.5P

BlackTom AI · Accepted Answer

A linear supply curve can be written Qs = aP + b. Use the two given (P, Qs) points to solve for a (slope) and b (intercept).

Relevant concepts:
- A straight line is uniquely determined by two points.
- Slope a = (change in Qs) / (change in P).
- Once a is known, substitute one point to solve for intercept b.

Step-by-step reasoning and calculations:
1. Read the supply data from the table: (P = 10, Qs = 5) and (P = 20, Qs = 10).
2. Compute the slope a:
   a = (Qs2 − Qs1) / (P2 − P1) = (10 − 5) / (20 − 10) = 5 / 10 = 0.5.
3. Substitute the slope into Qs = 0.5P + b and use one point to find b. Using (P = 10, Qs = 5):
   5 = 0.5(10) + b
   5 = 5 + b
   b = 0.
4. Therefore the linear supply equation is Qs = 0.5P + 0, i.e. Qs = 0.5P.

Verification:
- For P = 10: Qs = 0.5(10) = 5 (matches table).
- For P = 20: Qs = 0.5(20) = 10 (matches table).

Why this answer is correct:
- The slope 0.5 means quantity supplied increases by 0.5 units for each $1 increase in price, consistent with the two data points.
- The intercept is zero because the line passes through the origin given these observations.

Why other possible forms are incorrect:
- Any line with a different slope would not produce the observed change of 5 units in Qs when P increases by 10.
- Any nonzero intercept would fail to satisfy at least one of the two supplied points, so it cannot be the correct supply curve for these data.

Conclusion: The derived supply equation is Qs = 0.5P, which matches the provided answer.

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