Total revenue is in dollars and x is the number of units. Suppose that demand fo

Question

Total revenue is in dollars and x is the number of units. Suppose that demand for local cable TV service is given by p 80 0.4x where p is the monthly price in dollars and x is the number of subscribers (in hundreds) (a) Find the total revenue R (in hundreds of dollars) as a function of the number of subscribers (in hundreds) R(x) (b) Find the number of subscribers (in hundreds) when the company charges $50 per month for cable service. hundred subscribers Find the total revenue (in hundreds of dollars) for p-$50. hundred dollars (c) How could the company attract more subscribers? More subscribers are attracted by Select prices. (d) Find the marginal revenue (in hundreds of dollars) when the price is $50 per month hundred dollars Interpret this value (hundred) to (hundred) the revenue L-Select- (100)- If the number of subscribers Increases from What does this suggest about the monthly charge to subscribers? Increasing the number of subscribers will occur by raising the monthly charges. O Increasing the number of subscribers will occur by lowering the monthly charges

Explanation / Answer

a) TR = price x quantity = px = (80 - 0.4x)x = 80x - 0.4x2

b) p = 80 - 0.4x

50 = 80 - 0.4x

0.4x = 30

x = 30/0.4 = 300/4 = 75 hundred subscribers

TR = px = 50 x 75 = 3750

c) Decrease in price

d) TR = (80 - 0.4x)x = 80x - 0.4x2

MR = dTR/dx = 80 - 0.8x

when p = 50 then x = 75

MR = 80 - 0.8(75 hundred) = 80 - 60 hundred = 20 hundred dollars

If number of subscribers increases from 75 hundred to 80 hundred the revenue increases by

(80 x 50 - 75 x 50) = $ 250

Increasing the number of subscribers will occur by lowering monthly charges.

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