Question

You are the owner/manager of a small competitive firm that manufactures house paints. You and all...

You are the owner/manager of a small competitive firm that manufactures house paints. You and all your 1,000 competitors have total cost curves given by
TC = 63 + 7Q + 7Q2
and the industry is in long-run equilibrium.
Now you are approached by an inventor who holds a patent on a process that will reduce your costs by 20% at each level of output.


a. What is the most you would be willing to pay for the exclusive right to use this invention?


b. Would the inventor be willing to sell at that price?

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Homework Answers

Answer #1

Industry is in long run equilibrium. It means P=LRATC

ATC= TC/Q= 63/Q+7+7Q

dATC/dQ= - 63/Q^2+7=0

63/7=Q^2

Q= 3

P= LRATC= 63/3+7+7*3=21+7+21= 49

Find Q by using P= 49 and TCnew= 20%*TC=TC/5= 63/5+7Q/5+7Q^2/5

MC=dTCnew/dQ= 7/5+ 14Q/5

P=MR=MC

49=7/5+ 14Q/5

49*5=7+14Q

Q=238/14

Qnew= 17

profit with Qnew=

TR=P*Qnew= 49*17=833

TC= 63/5+7*17/5+7*(17)^2/5= 12.6+23.8+404.6= 441

Profit= TR-TC= 833-441=$392

a. The most you would be willing to pay for this exclusive right= $392

b. No, the inventor will not be willing to sell as it can sell to more than one firm.

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