Question

A monopoly firm faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is not required to be presented), either way, please provide a brief description of how you arrived at your results. Excel please!!!

a)   How much will the firm produce?
b)   How much will it charge?
c)   Can you determine its profit per day? (Hint: you can; state how much it is.)
d)   Suppose a tax of $1,000 per day is imposed on the firm. How will this affect its price?
e)   How would the $1,000 per day tax its output per day?
f)   How would the $1,000 per day tax affect its profit per day?
g)   Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price?
h)   How would a $100 per unit tax affect the firm’s profit maximizing output per day?
i)   How would the $100 per unit tax affect the firms profit per day?

Answer 1

A. The firm will produce profit maximizing output of 20 (=Q) units as can be seen from the table below.

B. It will charge the price at the profit maximizing output level i.e. $300

C. The profit earned by the monopolist is given by TR - TC at the output of 20 units. The profit is $4,000

D. A lump sum tax of $1,000 will shift the TC curve of the monopolist upwards by $1000. However, since the slope of the TC curve remains the same, the monopolist will continue to produce at the original level of equilibrium, i.e. output = 20 units and price = $300.

E. The output will remain same at 20 units

F. The profit will reduce by $1000 everyday.

Kindly up vote my answer.