Question

uppose the government imposes a tax of T dollars per unit on the monopolist, andtherefore the monopolist’s marginal cost is now6+T. Show that the monopolist willpass along half of the tax to its customers, i.e., show that the profit-maximizing price isnow15 + (T/2).

Answer 1

Step-by-step explanation:

A monopolist Inverse Demand Curve is Given as: P=24-Q

And we are also Given the Marginal Cost (MC) = $6

The Revenue of the Monopolist would be:

R=PXQ = 24Q - Q

Marginal Revenue= 24-2Q

A) Monopolist would produce at the price corresponding to the quantity of : MR=MC

24 – 2Q = 6

20 = 24 – 6 = 18

Q = 9

SO the Profit maximizing price would be: P=24-Q = 24-9 = 15

Thus profit maximizing price and Quantity are: P^*= $15 and Q^*=9

Profit = Revenue - Cost

Cost = Average Cost * Quantity = 6Q

Profit = 24Q-Q2-6Q = 18Q - Q2 = 18 X 9 -9

Profit = 81

Part B::

Now Government imposes a tax, on this monopolist, T.

So new MC= 6+T

Lets solve for Profit maximizing Price:

MR=MC

24-2Q=6+T

Q=\frac{18-T}{2}

and Price:

P=24-Q = 24-\frac{18-T}{2}

P=15+\frac{T}{2}

Thus Now the monopolist would charge Half of this tax from consumers.