Question

A monopoly firm faces a demand curve given by the
following equation: P = $500 - 10Q, where Q equals quantity sold
per day. It's marginal cost curve is MC = $100 per day. Assume that
the firm faces no fixed cost. Provide an explanation of the
results.

How much will the firm produce?

How much will it charge?

Can you determine its profit per day?

Suppose a tax of $1000 per day is imposed on the firm? How will
this affect its price?

How would the $1000 per day tax its output per day?

How would the $1000 per day tax affect its profit per day?

Now suppose a tax of $100 per unit is imposed. How will this affect
the firm's price?

How would a $100 per unit tax affect the firm's profit maximizing
output per day?

How would the $100 per unit tax affect the firm's profit per
day?

Answer #1

TR = 500Q-10Q^{2}

MR =500-20Q

To determine the profit maximizing quantity we will equate MR and MC

500-20Q = 100

400=20Q

Q= 20 units

Therefore, the firm will produce 20 units per day.

P=500-10*20 = $300

Therefore, the firm will charge $300 per unit.

Total cost = MC *Q = 100 *20 = $2000 per day

Total revenue = P*Q = 300*20 =$6000 per day

Profit per day = TR per day - Total Cost per day = 6000-2000 = $4000 per day

When a tax pf $1000 per day is imposed on the firm, TC= $2000+$1000 = $3000

Profit = $6000-$3000 = $3000

When profit = $4000, Q= 20

So, when profit = $3000, Q= 15.

P= 500-10*15 = $350

So when a tax of $1000 is imposed, the price increases to $350 per day and the output decreases to 15 units per day.

Profit = (15*350) - (100*15) = $3750

Therefore, the profit has reduced by $250.

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