Question #1 : Suppose that Shannon is the only economics tutor in Bucksnort and
ID: 1108574 • Letter: Q
Question
Question #1 : Suppose that Shannon is the only economics tutor in Bucksnort and therefore holds a monopoly on the sale of tutoring services. Suppose that Shannon can offer additional hours of tutoring at a constant marginal cost of $2 per hour and faces no fixed costs. Use the table below to answer the following questions Table: Demand for Economics Tutoring Quantity of Economics Tutoring Economic Price of s Tutoring per hour) 6 6 0 a) If Shannon acts as a classical monopolist, how many hours of tutoring services will she offer and what price per hour will she charge for tutoring? b) Suppose that Shannon can perfectly price discriminate by charging her customers their willingness to pay. How many hours of tutoring services will she now offer? c) Derive and compare Shannon's profits under classic monopoly pricing and first-degree price discrimination.Explanation / Answer
a) Marginal Cost(MC)=$2
Fixed Cost(FC)= 0
Marginal Revenue=MR
So, we know that for a monopoly profit maximisation occurs at MC=MR.
Again, the necessary condition for a monopoly is that the price should be greater than the marginal revenue.i.e., P=MR.
In the question above they are saying that the marginal cost is $2 and therefore, the price has to be greater than that MC. Or, P>(MR=MC).
Now, from the given data at Price$2 the quantity (hours) is 4. So, if we find the profit ()= 0( Total revenue=price*quantity and total cost which we find from the marginal cost (MC) to be 2q by the method of integration as marginal cost MC=d(total cost)/d(quantity))
So, at price 2 we have a profit = 2*4-2*4=8-8=0
At price$3 the profit is = 3*3-2*3=9-6=3
At price $4 the profit =4*2-2*2=8-4=4
At price $5 the profit =5*1-2*1=5-2=3
At price $6 the profit = 6*0-2*0=0
We see that from price $5 the profit starts falling and at price $4 the profit is maximum.
The first order condition for price $4 is 2.
Hence, if Shannon acts as a classical monopolist, then, she will take $4 per hour price and teach for 2hours.
b) The perfect price discrimination also known as the first degree price discrimination is where the producer charges the reservation price(maximum willingness to pay) by the buyer and finally the producer extracts the whole of the consumer surplus.
In case of first degree price discrimination the monopolist will produce at price= marginal cost. So, Shannon will start to teach at price $2 for 4hours and will increase her profit from here on according to the willingness of the students to pay.
c) Shannon's profits for the first degree price discrimination will be 0+3+4+3=10. And the profits for the monopoly pricing is already done in part a.