In the reclining chair industry (which is perfectly competitive), two different technologies of production exist.These technologies exhibit the following total cost functions:
C1(Q)= 1,000 + 600Q - 40Q2 + Q3
C2(Q)= 200 + 145Q- 10Q2 + Q3
Due to foreign competition, the market price of reclining chairs has fallen to $190.In the short run, firms using technology 1
A)and firms using technology 2 will remain in business.
B)will remain in business and firms using technology 2 will shut down.
C)will shut down and firms using technology 2 will remain in business.
D)and firms using technology 2 will shut down.
E)More information is needed to make a judgment.

Question

In the reclining chair industry (which is perfectly competitive), two different technologies of production exist.These technologies exhibit the following total cost functions: 
C1(Q)= 1,000 + 600Q - 40Q2 + Q3
C2(Q)= 200 + 145Q- 10Q2 + Q3
Due to foreign competition, the market price of reclining chairs has fallen to $190.In the short run, firms using technology 1
A)and firms using technology 2 will remain in business.
B)will remain in business and firms using technology 2 will shut down.
C)will shut down and firms using technology 2 will remain in business.
D)and firms using technology 2 will shut down.
E)More information is needed to make a judgment.

Quizplus · Accepted Answer

Firms will shut down in the short run if the price is below the average variable cost (AVC). For both technologies, we need to find the AVC and compare it to the market price of $190. The AVC is derived from the variable part of the total cost function, ignoring the fixed costs.For technology 1, the variable cost is $600Q - 40Q^2 + Q^3. The AVC would be this expression divided by Q, which simplifies to $600 - 40Q + Q^2. Without specific quantities, we can't calculate an exact AVC, but we know it decreases initially as Q increases due to the negative quadratic term.For technology 2, the variable cost is $145Q - 10Q^2 + Q^3. The AVC simplifies to $145 - 10Q + Q^2. This AVC starts higher than the price of $190 for low quantities and may decrease below $190 as Q increases, but without specific quantities, it's challenging to determine the exact point.Given the complexity of the cost functions and without specific output levels (Q), it's difficult to precisely determine the AVC for each technology at various output levels. However, the decision on whether to shut down depends on whether the price covers the AVC. Since we lack specific quantities and the functions are complex, more information is indeed needed to make a judgment. However, based on the information provided and the typical approach to such problems, the correct choice would be to compare the market price to the AVC of each technology to determine if they would shut down or remain in business. Given the lack of specific data to calculate AVC for each technology at the market price of $190, the most accurate answer with the information provided would be that more information is needed (E).

In the Reclining Chair Industry (Which Is Perfectly Competitive), Two