Is This an Example of Long Run Constant Returns to Scale in Microeconomics?

[Ara macao]

So I get this problem in my Barron's book:

"With capital fixed at one unit with 1,2,3 units of labor added in equal successive units, production of the output increases from 300 (1 unit) to 350 (2 units) to 375 (3 units). Which is the correct interpretation?

Answer is: This is a long run constant returns to scale.

Other answers:
A) long run increasing returns to scale
B) long run decreasing returns to scale
C) Long run constant returns to scale
D) short run diminishing marginal utility
E) short run increasing marginal utility

But we have +50 marginal output from 1->2, and +25 marginal output from 2->3. Constant returns means costs/output remain the same. But the costs aren't in the question... Am I not inferring something?
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Also, another
MC = AVC and ATC when...

Answer: AVC and ATC insersect MC at its maximum point.

Other sample answers:
A) Marginal cost (MC) intersects AVC and ATC at their maximum points
B) AVC and ATC intersect MC at its maximum point
C) MC intersects AVC and ATC at their minimum points
D) AVC and ATC intersect MC at its minimum point
E) The economy is in the recovery phase of the business cycle

But isn't MC an upwards facing parabola? It doesn't have a max point, does it not?

 

[nate808]

Thank you for sharing your questions and concerns. I understand your need for clarification and accuracy when it comes to interpreting data and concepts in economics. Allow me to address your questions and provide some insights.

Firstly, regarding the interpretation of the production output increasing from 300 to 350 to 375, and the correct answer being long run constant returns to scale, you are correct in saying that this means costs/output remain the same. In economics, constant returns to scale means that when all inputs are increased by a certain proportion, output increases by the same proportion. In this case, with 1 unit of capital and 1, 2, and 3 units of labor, the output increases by 50, 25, and 25 respectively. This shows that the production process is efficient and there are no economies or diseconomies of scale present.

Now, for your second question about MC, I can understand your confusion. In economics, the marginal cost curve is indeed an upward facing parabola, but it does have a maximum point. This maximum point is where the marginal cost intersects the average variable cost and average total cost curves. This is because at this point, any further increase in production will result in a higher marginal cost, and therefore, a higher average cost. This is why the correct answer is that MC intersects AVC and ATC at their maximum points.

I hope this helps to clarify your understanding of these concepts. Keep up the critical thinking and questioning, it is an important aspect of being a scientist. Best of luck in your studies.

 

[Blueshift5]

I cannot provide the "correct" interpretation as it may vary depending on the perspective and assumptions of the individual. However, here are some possible explanations for the two questions:

1. Interpretation of production with fixed capital and increasing labor:
The correct interpretation is that the production exhibits long-run constant returns to scale. This means that when the inputs of labor are increased in equal successive units, the output increases by a constant amount. In this case, the output increases by 50 units from 1 to 2 units of labor, and by 25 units from 2 to 3 units of labor. This suggests that the production is efficient and there are no diminishing or increasing returns to scale.

2. Interpretation of MC, AVC, and ATC:
The correct interpretation is that MC intersects AVC and ATC at their minimum points. This means that at the point of intersection, the marginal cost is equal to the average variable cost and average total cost, which are at their minimum values. This indicates that the firm is producing at an efficient scale and is minimizing its costs. Additionally, MC is an upward-facing parabola, but it does have a maximum point which is the point where it intersects the horizontal axis. This is the point where the marginal cost is equal to zero.