Asked by Juanita Soriano on May 14, 2024
Verified
A firm has the long-run cost function C(q) 7q2 175.In the long run, it will supply a positive amount of output, so long as the price is greater than
A) $70.
B) $148.
C) $35.
D) $140.
E) $75.
Long-Run Cost Function
A concept that describes how the total production costs of a firm change based on output levels, considering all inputs as variable in the long term.
Output Supply
The total amount of a good or service that producers are willing and able to sell at a given price over a certain period of time.
Price
The financial expenditure needed to acquire a good or service.
- Comprehend the circumstances that determine a firm's decision to engage in production in both the short term and long term.
- Investigate how businesses operate economically across various market structures, such as competitive, monopolistic, and oligopolistic environments.
Verified Answer
JS
Jakob SteinMay 16, 2024
Final Answer :
A
Explanation :
In the long run, a firm will supply a positive amount of output if the price is greater than the minimum average cost. The given cost function is C(q)=7q2+175C(q) = 7q^2 + 175C(q)=7q2+175 . To find the minimum average cost, we first find the average cost (AC) function by dividing the total cost by q: AC=7q2+175q=7q+175qAC = \frac{7q^2 + 175}{q} = 7q + \frac{175}{q}AC=q7q2+175=7q+q175 . To find the minimum of this function, we take its derivative with respect to q and set it equal to zero: AC′=7−175q2=0AC' = 7 - \frac{175}{q^2} = 0AC′=7−q2175=0 . Solving for q gives q2=1757=25q^2 = \frac{175}{7} = 25q2=7175=25 , so q=5q = 5q=5 . Substituting q = 5 back into the AC function gives the minimum average cost: ACmin=7(5)+1755=35+35=70AC_{min} = 7(5) + \frac{175}{5} = 35 + 35 = 70ACmin=7(5)+5175=35+35=70 . Therefore, the firm will supply a positive amount of output as long as the price is greater than $70.
Learning Objectives
- Comprehend the circumstances that determine a firm's decision to engage in production in both the short term and long term.
- Investigate how businesses operate economically across various market structures, such as competitive, monopolistic, and oligopolistic environments.