Answer to Question #165697 in Microeconomics for Juliana Namagembe

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.

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

Profit maximizing firm will always produce where

marginal cost (MC)= marginal revenue (MR)

A monopoly will face a MR curve with twice the slope of the demand curve.

Therefore

(a)$MR = TR'(Q)$

$MR=500-2Q$

$Mc=100$

$500-2Q=100$

$500-100=20Q$

$Q = 20 units$

(b)

$P = 500-10(20)$

$=300$

(C)

MC = ATC

so its profit per day is:

TP = (P - MC)*Q

$=(300-100)*20=4000$

(d)If a tax of $1,000 per day is imposed on the firm, then its price will increase.

$P=500-(10*15)=350$

e) The $1,000 per day tax would decrease its output per day.

Tax of $1000 reduces profit to $3000 from $4000

If Q of 20 produces profit of $4000, then $3000 will be produced by

$(20x3000)/4000 =15$

f) The $1,000 per day tax would decrease its profit per day.

$4000−1000=3000$

g) If a tax of $100 per unit is imposed, then the firm’s price will increase.

$P=500-(10*19.5)=305$

h) A $100 per unit tax would decrease the firm’s profit maximizing output per day

Tax of $100 reduces profit to

($4000-100) =3900$

If quantity 20 produces profit of $4000, then $3900 is produced by

$(3900x20)/4000 = 19.5$

(I) A $100 per unit tax would decrease the firm’s profit per day.

$4000-100=3900$