Suppose a farmer is a price taker for soybean sales with cost functions given by the following:

TC = 0.1q2 + 2q + 30

MC = 0.2q + 2

The firm's supply curve is given by

Question

Suppose a farmer is a price taker for soybean sales with cost functions given by the following:

TC = 0.1q2 + 2q + 30

MC = 0.2q + 2

The firm's supply curve is given by

BlackTom AI · Accepted Answer

A price-taking firm chooses output where P = MC (provided price covers average variable cost).

1. Relevant knowledge points and concepts
- For a competitive (price-taking) firm, the short-run supply curve is the portion of the marginal cost (MC) curve above the shutdown point (minimum average variable cost, AVC).
- Given total cost TC = 0.1q^2 + 2q + 30, variable cost VC = 0.1q^2 + 2q and AVC = VC/q = 0.1q + 2.
- Marginal cost is given: MC = 0.2q + 2.

2. Complete reasoning process step by step
- Set price equal to marginal cost for positive output: P = MC.
- Substitute MC: P = 0.2q + 2.
- Solve for q in terms of P.

3. Calculations with intermediate steps
- P = 0.2q + 2
- P - 2 = 0.2q
- q = (P - 2) / 0.2
- Since 1/0.2 = 5, q = 5(P - 2) = 5P - 10.

4. Why the correct answer is correct
- This algebra shows the firm’s supply relation (inverse MC) is q = 5P - 10. However, the firm will only produce if price covers AVC. AVC = 0.1q + 2 is minimized at q = 0 (it's linear increasing), so the shutdown price is AVC_min = 2. At P = 2, the formula gives q = 0; for P < 2 the firm shuts down (q = 0). Thus the supply curve is q = 5P - 10 for P ≥ 2 (and q = 0 for P < 2). The multiple-choice option gives the algebraic supply function q = 5P - 10, which matches the derived relation.

5. Why the other options are incorrect
- "q = 0.2P + 2" incorrectly treats MC as q = 0.2P + 2 instead of solving P = 0.2q + 2; it confuses coefficients.
- "q = 10P – 2" has the wrong slope and intercept (factor 10 rather than 5 and wrong constant).
- "q = 2P – 5" also has incorrect slope/intercept; none of these follow from P = 0.2q + 2.

6. Conclusion
The firm’s supply function is q = 5P – 10 (with the practical constraint q = 0 for P < 2). This matches the provided answer q = 5P – 10.

Suppose a farmer is a price taker for soybean sales with cost functions given by the following: TC = 0.1q2 + 2q + 30 MC = 0.2q + 2 The firm's supply curve is given by单项选择题

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Suppose a farmer is a price taker for soybean sales with cost functions given by the following: TC = 0.1q2 + 2q + 30 MC = 0.2q + 2 The firm's supply curve is given by单项选择题

类似问题

The bond supply curve is ________ sloping, indicating a ________ relationship between price and quantity supplied:

What does a supply curve show?

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If there are 100 identical firms in the rag industry, and each firm is willing tosupply 10 rags at any price. The curve of the inverse market supply will (choose all correct answers):

3. The speaker seems most disappointed about:

更多留学生实用工具

希望你的学习变得更简单

The bond supply curve is sloping, indicating a relationship between price and quantity supplied: