Question 7.54 Choose the correct answerSuppose that the marginal cost of producing a pound of cereal is $2, irrespective of the level of output, but there are also some fixed costs of production. Read the following statements and select the correct one.

Question

BlackTom AI · Accepted Answer

Marginal cost is the additional cost of producing one more unit. If MC = $2 for every extra pound, the MC curve is a constant horizontal line at $2.

1. Relevant knowledge points and concepts
- Total cost (TC) = Fixed cost (FC) + Variable cost (VC).  
- Marginal cost MC = d(TC)/dQ.  
- If MC is constant, VC is linear in output.  
- Average cost AC = TC/Q = FC/Q + VC/Q.

2. Step-by-step reasoning
- Given MC = 2 for all Q, integrate to get TC: TC(Q) = 2Q + C, where C is a constant. That constant equals fixed cost (FC), so TC(Q) = FC + 2Q.
- Variable cost VC(Q) = 2Q and FC > 0 by the problem statement.

3. Calculations and intermediate steps
- TC(Q) = FC + 2Q.
- AC(Q) = TC/Q = (FC + 2Q)/Q = 2 + FC/Q.
- dAC/dQ = d(2 + FC/Q)/dQ = -FC/Q^2, which is negative for FC > 0, so AC strictly decreases with Q and approaches 2 as Q → ∞.
- Solve MC = AC: 2 = 2 + FC/Q ⇒ FC/Q = 0 ⇒ requires FC = 0 or Q → ∞. With positive FC, there is no finite Q where MC intersects AC.

4. Why the correct answer is correct
- Because MC is constant at $2 regardless of Q, its graph is a horizontal straight line at $2. This directly matches option c.

5. Why the other options are incorrect
- a: “MC intersects AC at its minimum” is false here because AC decreases monotonically toward 2 and has no finite minimum where MC intersects (unless FC = 0).  
- b: “AC is U-shaped” is false: AC = 2 + FC/Q is strictly decreasing for FC > 0, not U-shaped.  
- d: “TC is an upward-sloping straight line through the origin” is false because TC = FC + 2Q has an intercept FC, so it does not pass through the origin when FC > 0.

6. Conclusion
All reasoning confirms option c: The marginal cost curve is a horizontal straight line. This matches the provided correct answer.

Question 7.54 Choose the correct answerSuppose that the marginal cost of producing a pound of cereal is $2, irrespective of the level of output, but there are also some fixed costs of production. Read the following statements and select the correct one.单项选择题

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