Assume that a monopolist faces a demand curve for its product given by: p=100?1q p = 100 – 1 q Furth

Assume that a monopolist faces a demand curve for its product given by:

p=100?1q

p

=

100

1

q

Further assume that the firm’s cost function is:

TC=550+9q

T

C

=

550

+

9

q

Using calculus and formulas (but no tables or spreadsheets) to find a solution, how much output should the firm produce at the optimal price?

Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should then round to the nearest cent Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items

Hint: Define a formula for Total Revenue using the demand curve equation Then take the derivative of the Total Revenue and Total Cost formulas Use these derivative equations to perform a marginal analysis