Perfect Competitive Market Case Study

Register to read the introduction… Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost.
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
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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)

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