Question

# A monopoly firm faces a demand curve given by the following equation - P = \$500...

A monopoly firm faces a demand curve given by the following equation - P = \$500 - 10Q, where Q equals quantity per day. Its marginal cost curve is MC = \$100 per day. Assume that the firm faces no fixed cost. Please answer each question mathematically.

a). Now suppose a tax of \$100 per unit is imposed. How will this affect the firms price?

b). How would a \$100 per unit tax affect the firms profit maximizing output per day?

c). How would the \$100 per unit tax affect the firms profit per day?

Given That:-

A monopoly firm faces a demand curve given by the following equation - P = \$500 - 10Q, where Q equals quantity per day. Its marginal cost curve is MC = \$100 per day. Assume that the firm faces no fixed cost. Please answer each question mathematically.

Demand Curve eqn P = \$500 - 10Q,.

Q = quantity sold per day

X10 fixed cost

Sol:-

Total Revenue (TR) =

= 500 Q - 10 Q2

Marginal Revenue (MR) = First derivative of TR

=

= 500 - 20 Q

* MR = MC

500 - 20 Q = 100 Q = 400/20 = 20

Price = P = 500 - 200 = \$ 300

(a)

\$100 per day tax - Impact on price

Advalorem taxes : are charged as a proportion of the price

eg: VAT

Two types of prices

firm price

consumer price

Relation between firm price & consumer price

Pc = consumed price

Pf = firm price

= 33.33 %

1.333 Pf = 500 - 10Q

Pf = 375 - 7.5Q

TR = 375 Q - 7.5 Q2

MR = 375 - 15 Q

MR = MC

375 - 15 Q = 100

275 = 15 Q Q = 275/15 = 18.33

then price = 375 - 7.5(18.33)

= 375 - 137.5

= 237.5

The Affect of &100 per day tax is that price of firm decreases to \$ 237.5 from \$ 300

(b)

Specific taxes : Charged on output here consumer demand function remains constant ie

Pc = \$ 500 - 10 Q but

Pf = \$ 500 - 10Q - y y = specific tax

Pf = \$ 500 - 10Q - 100/20

Pf = 495 - 10Q

TR = 495 Q - 10 Q2

MR = 495 - 20 Q

MR = MC

495 - 20 Q = 100

395 = 20 Q

Q = 395/20 = 19.75

So the firm produces output of 19.75 units

(c)

Affect on profit

We see that with \$100 per day tax affect the price from \$ 300 - 237.5

output from \$ 20 units - 19.75 units

Profit decreases to the firm.