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Determination of price

I need help figuring out the following practice problem - I have solved for some solutions but am not sure of my answers. Please look below and solve alebraically - show work so I know how you got your answers.

Question

P = 28 - 0.0008Q
TC = 120,000 + 0.0006Q2

Where Q is the number of cable subscribers and P is the price in dollars of basic monthly Clear Vision, Inc. cable service.

a. How many cable subscribers would be expected if Clear Vision was allowed to operate completely unregulated? What price will be charged?

I came up with:
MR=MC
28-0.0016Q=0.0012Q
Q=10,000 - therefore, there are 10,000 cable subscribers if Clear Vision is allowed to operate completely unregulated

b. How many cable subscribers would be expected if Clear Vision acted like a perfect competitor? What price will be charged

I came up with
MR=MC
0.0012Q = 28-0.0008Q
Q=14,000 - therefore, there should be 14,000 cable subscribers if Clear Vision acted like a perfect competitor

c. How many cable subscribers would be expected if the city government did not allow the firm to charge more than $18 for price?

I came up with:
P=MC
P = 28 - .0008Q
18 = 28 - .0008Q
12,500 = Q

d. Calculate the profit if Clear Vision was allowed to operate completely unregulated?

I came up with:
Profit = TR - TC
TR = P(Q)
Q = 10,000
P = 28 - .0008(Q)
P = 28 - .0008(10,000) = 28 - 8 = $20
TR = P(Q) = $20(10,000) = $200,000
TC = $120,000 + $.0006Q2
TC = $120,000 + $.0006(10,000)2
TC = $120,000 + $.0006(100,000,000)
TC = $120,000 + $60,000
TC = $180,000
Profit = TR - TC = $200,000 - $180,000 = $20,000

e. What would be the deadweight loss if Clear Vision acted like a perfect competitor?

I came up with:
There is no deadweight loss if Clear Vision acted like a Perfect Competitor. There is no consumer or producer surplus in a perfectly competitive market.

Thanks for your help.

Solution Preview

I need help figuring out the following practice problem - I have solved for some solutions but am not sure of my answers. Please look below and solve alebraically - show work so I know how you got your answers.

Question

P = 28 - 0.0008Q
TC = 120,000 + 0.0006Q2

Where Q is the number of cable subscribers and P is the price in dollars of basic monthly Clear Vision, Inc. cable service.

a. How many cable subscribers would be expected if Clear Vision ...

Solution Summary

This explains the determination of price under various situations

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