P = 1200 - 6Q (demand curve for the monopoly) C = 8600 + 20Q + Q 2 (total cost f

Question

P = 1200 - 6Q (demand curve for the monopoly)

C = 8600 + 20Q + Q2 (total cost function for the monopoly)

MC = 20 + 2Q (marginal cost function for the monopoly)

**Please round all answers to TWO decimal places**

To maximize profit, the monopolist should produce ___ units of output.

The company's profit -maximizing price is $___

The monopolist's profit is $___

Suppose the government imposes a specific tax of $200 per unit on the monopolist. To maximize profit, the monopolist should now produce ___ units of output. When the tax is imposed, the monopolist's profit-maximizing price becomes $___. As a result of the tax, the monopolist raises its price by _____ (Choose one: more than the tax/the same amount as the tax/less than the tax).

Explanation / Answer

To maximize profit, the monopolist should produce 84.28 units of output.

The company's profit -maximizing price is $694.32

The monopolist's profit is $42645.61

Explanation

In a monoplooy the profit will be maximised where MR=MC

MC= 20+2Q and

for a linear downward sloping demand curve, the MR has the same y-intercept and twice the slope of this demand curvefor a linear downward sloping demand curve.

So MR= 1200-12Q

So Profit will be maximised where MR=MC

1200-12Q = 20+2Q

=-14Q=-1180

Q=1180/14 = 84.28

Use this quantity and the demand curve to find the monopolist’s profit maximizing price: P = 1200 – 6Q or P = $694.32 per unit.

Profit is = TR – TC: so Profit = ($694.32per unit)(84.28 units) – (8600 + 20Q + Q2)

=($694.32per unit)(84.28 units) - ( 8600 +20(84.28) +(84.28) (84.28) =$41128.57

Incidence of Taxation

Suppose the government imposes a specific tax of $200 per unit on the monopolist. To maximize profit, the monopolist should now produce 70 units of output. When the tax is imposed, the monopolist's profit-maximizing price becomes $780. As a result of the tax, the monopolist raises its price by less than the tax

The monopolist must remit $200 to the goverment for every unit it sells. Therefore, the firm's MC is is increased by the amount of the tax.

So the new MC =220+2Q

Now to find out we neew to equate MR= new MC

1200-12Q = 220+2Q

Q = 70 units

Use this quantity and the demand curve to find the monopolist’s profit maximizing price: P = 1200 – 6Q or P = $780 per unit.

Profit is = TR – TC: so Profit = ($780 per unit)(70 units) – (8600 + 20Q + Q2)

=$39700

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