In: Economics
Regulating a Monopoly
Say you have a monopoly that provides a transportation service to a city.
Total investment in infrastructure and busses amounts to $65,000,000
The company sells tickets to riders for a fixed price- i.e. one monthly price for any length journey
Monthly demand for tickets is
P = 20.25 - .00005Q
Where P = price of a ticket and Q the number of tickets
TC = $4,625,000 + 30Q + .0003Q2 MC =
30 + .0006Q
A)
Without regulation, how much would a monopoly charge per ticket and how many
tickets would it make available?
B)
What would be its ROI?
C)
Assume that you want to regulate the monopoly so that its return on investment does
not exceed 8%. How many units must it produce and how much would it charge for
each unit?
ANSWER
GIVEN THAT
Now to derive MR we need to calculate total revenue generated i.e.
= Price*Quantity
And MR is Total revenue of qth unit less the total revenue from selling q+1th unit.
Or, MR= dTR/DQ
Or, MR= d(20.25-0.00005Q)Q/dQ
Or MR= 20.25Q-0.00005Q2/dQ
Or, MR= 20.25- 0.0001Q
On the other hand, similarly, Marginal cost can be calculated using total cost,
Where, MC is given as,
MC= 30+0.0006Q is the cost of producing each unit.
Now at equilibrium without regulation,
MR=MC
Implies,
20.25- 0.0001Q = 30+0.0006Q
Or, 20.25-30 = (0.0006+0.0001)Q
Or, -9.75 = 0.0007Q
Or, Q= -13,928.57
Due to the specification the quantity in figures calculates to be dubious.
It can be seen that the equilibrium cannot be in negative due to common sense, hence we infer that the total production for would be 13,928 units for MR=MC.
Using the Q we can calculate per unit price that is,
P= 20.25-0.00005Q
Supplanting Q gives
P= 20.25- 0.6964
Or, P= 19.55
That is, RoI = (Current Value of Investment - Cost of Investment) / Cost of Investment
Now current value of the investment would be
Total quantity*per unit price
Or, Q*P= 13,928 *19.55
Or, current value = 272292.4
Therefore, RoI= (272292.4-65000000)/ 65000000
Or, RoI= -0.9958
Or, taking modulus, to remove negative,
Return on investment is 0.99% per annum
Or, alternatively,
Using the TC as the Cost of investment,
TC= $4,625,000 + 30(13928) +0 .0003(13928)2 = 5101037
Implies,
RoI = (Current Value of Investment - Cost of Investment) / Cost of Investment
RoI= (272292.4-5101037)/5101037
And the return on investment is= -0.94662,
Again, removing negative, RoI is 0.94%
0.8= (x-65000000)/ 65000000
Or, 0.8*65000000= x -65000000
Or, 52,000,000+65000000=x
Or, x = 117000000 is the total revenue that can be generated,
Thus, If it keeps its price fixed, it can sell 5,984,655 (approximate)
Or if it wants to sell 13,928 units, it can charge a price (117000000/13928)= 8400 or $84 per unit.
Because the monopoly cannot decide both price and quantity together.