Comcast Center City Philadelphia is dominated by (and home to) Comcast, which of
ID: 1137722 • Letter: C
Question
Comcast Center City Philadelphia is dominated by (and home to) Comcast, which offers Internet and Television to households. The company's marketing group currently estimates aggregate monthly demand for cable and internet bundles by Center City households is P 130 15 where the quantity is in thousands of households and the price is in dollars. The marginal cost of supplying services is a constant $30 per household per month a Solve for Comcast's revenue function, marginal revenue function, optimal price to charge in this market, and monthly profits R(O) MRCO) Profits b. Sean, an OSU Econ major doing an internship at Comcast, warns the company that people in their 20s and early 30s are "cord-cutters people who have lower demand for traditional cable service due to streaming services like Netflix and Hulu. He devises an experiment where a random sample of young Philadelphians are given discount coupons for Comcast service, and compared the uptake between that group and a control group. The results are below Group Control Discowr$ Price As found in Part (a) $10 off price found in Part (a) Uptake (purchase rate) 50% 65% Based on this, and what Sean remembers about the Inverse Elasticity Pricing Rule from Econ 5700, what can you say about the current price being offered to young Philadelphians? o It is the correct price to be charging them It is not the correct price, and he discounted price is better and the discounted price is worse o It is not the correct price, Why?Explanation / Answer
1.a)
Revenue is given by:
R(Q) = P.Q
Substituting the demand function in place of P, we get,
R(Q)= (130-2/15Q)Q
R(Q)=130Q-2/15Q2
1. b)
MR(Q) =?
Marginal revenue is the first derivative of the total revenue function.
So calculating the first derivative of the revenue function, R(Q), we get:
MR(Q)=d/dQ(130Q-2/15Q2)
MR(Q)= 130-4/15Q
1.c)
Price is equal to average revenue. We have Q=375 from part d0, so we substitute this value in the first equation,
so we get,
P=130-2/15Q
P=130-2/15*375
P=130-2*25
P=130-50
P=60
Therefore, Price is equal to 60.
1.d
In order to calculate profit maximization, Marginal revenue should be equal to marginal Marginal cost.
Equating both, MR and MC,
MR=MC,
130-4/15Q=30
130-30=4/15Q
100=4/15Q
This implies 4/15Q=100
4Q=100*15
Q=100*15/4
Q= 375
Therefore, profit maximizing Price is 60 and Quantity is 375.
Profits= (P-Cost)*Q
Profits=(60-30)*375
Profits=30*375=11250
Total Profits = 11,250