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
a) How much will the firm produce?
i) Profit maximizing firm will always produce where marginal cost = marginal revenue (MC=MR) ii) A monopoly will face a MR curve with twice the slope of the demand curve. Therefore
MR = 500+ 2x …show more content…
How will this affect its price?
i) Increase in tax reduces the output and raises the price. ii) P = $500 − 10Q iii) From (e) below, quantity is 15 iv) Therefore, P=500-(10x15) = $350
e) How would the $1,000 per day tax 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.
Therefore, output reduces to 15
f) How would the $1,000 per day tax affect its profit per day?
P=TR-TC
P= (15 x 350) - (100x15) = 5250-1500 = $3750
Reduction in profit is $(4,000-3750) = $250
g) Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price?
i) Tax of $100 reduces profit to $(4000-100) =$3900 ii) If quantity 20 produces profit of $4000, then $3900 is produced by (3900x20)/4000 = 19.5
h. How would a $100 per unit tax affect the firm’s profit maximizing output per day?
Tax of 100 per unit on 200 reduces profit to $(4000-2000)=2000
If quqntity of 20 producers profit of 4000$ then $2000is produced by (2000*20)/4000=10
There for P= 500-(10*10)