Suppose that the potential demand for a piece of software is given by QD(P) = 4,

Question

Suppose that the potential demand for a piece of software is given by QD(P) = 4,000 -4P. The software will cost $50,000 to develop. Once it is developed, the software can be distributed over the internet. (c) Assume the software has been developed. Find the equilibrium price and quantity for the software in a competitive market. PCE = QCE = (d) Find the consumer surplus (CS) at the price and quantity from part (c). CS = (e) What will the consumer surplus actually be if the software developer knows there will be a competitive market? Explain your answer. CS =

Explanation / Answer

Q = 4,000 – 4P

P = 1,000 – 0.25Q

TR = PQ = 1,000Q – 0,25Q^2

MR = Derivative of TR with respect of Q

       = 1,000 – 0.50Q

TC = 50,000

MC = Derivative of TC with respect of Q

       = 0

The equilibrium condition is MR = MC

1,000 – 0.50Q = 0

0.50Q = 1,000

Q = 2,000

Putting Q = 2,000 in P = 1,000 – 0.25Q

P = 1,000 – 0.25 × 2,000

   = 500

Answer: The equilibrium price is $500 and Quantity is 2,000 units.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.