Question

Lyft produces a software product that is protected by a patent (there are no alternatives to this product). The inverse demand curve for this software is given by P = 100 − Q + A, A is a measure of quality, P is price, and Q is quantity. The constant marginal cost of the software is $10 and the cost of quality is given by C(A) = A². The producer incurs fixed costs, F, for research and development (R&D).

1. Why is this a monopoly?

2. Write the profit equation for the producer.

3. Given the equation above, what are the producer’s profits? What level of quantity and quality should the producer choose? What price can the producer charge for both of quantity and quality?

4. The producer is accused of selling the product at a hiked up price. The producer states the price covers its research and development costs. Is this a valid arguement? Why or why not? How so is the price "hiked up"?

Answer 1

1). Because there is only one producer in this good market industry.

2)profit = TR - TC

TR=p*q=(100-q+A)*q=100-q2+Aq

TC=fixed cost + variable cost + quality cost=F+ Cq+A2=F+10q+A2

Profit=100q-q2+Aq-10q-A2-F

3) DERIVATIVE of profit function with respect to q, and put equal to zero,

100-2q+A+10=0

q=50+0.5A+5

Derivative of profit function with respect to A and put EQUALS to zero,

q-2A=0

A=0.5q

Putting A into q,

q=50+0.5(0.5q)+5

0.75q=55

q=55/0.75=220/3=73.33

A=(220/3)*0.5=110/3=36.66

P=100-220/3+110/3=100-110/3=190/3=63.33

Profit =100*73.333-(73.33)^2+36.33*73.33-10*73.33-(36.33)^2-F=2590.82

4)No, as we saw ,while determining the price , QUANTITY and quality ,we ignore the fixed cost of research and development .there is no reason ,the hiked price is because of research and development cost.

The price is hiked up because ,producer is selling very few QUANTITY to maximize its profit ,so lesser availability of good ,higher will be price.