A medium sized city is considering offering exclusive rights to CableNet, a cabl

Question

A medium sized city is considering offering exclusive rights to CableNet, a cable television carrier.

The demand function for cable in this city is: P= 28- 0.0008Q;

 The resulting marginal revenue function is: MR = 28 - .0016Q ; 

Cablenet's marginal cost function is MC= 0.0012Q

(Where Q = the number of clbe subscribers and P = the price of basic monthly service.

1. If Cablenet has exclusive rights, how much will they charge per month: How many people will subscribe at this price?

2. If the mayor of this city wants to maximize surplus what price per month should she mandate that CableNet charge? How many people will subscribe at this price?

3. What is the gain in surplus from regulating the CableNet's price?

4. How much is the monopoly worth to CableNet (i.e. how much will they spend lobbying the government not to regulate their price)?

Explanation / Answer

1. Set MR=MC 28 - .0016Q = 0.0012Q 28 = 0.0028Q Q = 28/0.0028 Q* = 10,000 Plug this into demand P= 28- 0.0008Q P= 28- 0.0008*10000 P* = 20 2. To maximize surplus, set P=MC 28- 0.0008Q = 0.0012Q 28 = 0.0020Q Q = 28/0.0020 Q` = 14000 Plug this into demand P = 28- 0.0008Q P = 28- 0.0008*14000 P` = 16.8 3. The gain in surplus is equal to the dead weight loss without regulation. It is the formula for a triangle with linear demand curves. DWL = (1/2)*DQ*(P*-MC), where DQ is the change in quantity from before and after regulation and (P*-MC) is the difference between the price and marginal cost before regulation. DQ = 14000-10,000 DQ = 4000 (P*-MC) = 20 - 0.0012Q* (P*-MC) = 20 - 0.0012*10000 (P*-MC) = 8 DWL = (1/2)*DQ*(P*-MC) DWL = (1/2)*4000*8 DWL = 16000 4. This is the change in producer surplus. MC* = 0.0012*10000 MC* = 12 The old producer surplus is: PS1 = (P*-MC)Q* + (1/2)MC*Q* PS1 = (20-12)*10000 + (1/2)*12*10000 PS1 = 140000 The new producer surplus is: PS2 = (1/2)P`Q` PS2 = (1/2)16.8*14000 PS2 = 117600 PS1 - PS2 = 140000 - 117600 PS1 - PS2 = 22400 So, the firm would be willing to spend up to $22,400 in order to avoid regulation. This is why cable companies fund political campaigns.

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