Question

Assume that a monopolist considering to spend 500.000 usd on large campaign to promote the their products.
The demand curves are defined by
p = 150 - 3q, where q is the output-quantity in 1000-usd. By executing the campaign the firm expects the new demand-curves to be
p = 400 - 4q.
Their total cost are c(q) = 30q, and the 500.000 usd are not included in this.

a) If the expectations regarding the demand-curves are correct, is it beneficial for the company to do the campaign?

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I'm really fairly certain that it is beneficial but I'm uncertain how to explain it using the theory of microeconomics.

Answer 1

Total cost including campaign cost (TC) = 500 + 30q

Marginal cost (MC) = dTC/dq = 30

Monopolist will maximize profit (or minimize loss) by equating Marginal revenue (MR) with MC.

Before the campaign,

Total revenue (TR) = p x q = 150q - 3q²

MR = dTR/dq = 150 - 6q

Equating with MC,

150 - 6q = 30

6q = 120

q = 20

p = 150 - (3 x 20) = 150 - 60 = 90

TR = 90 x 20 = 1,800

TC = 30 x 20 = 600

Profit = TR - TC = 1,800 - 600 = 1,200

After the campaign,

New TR = 400q - 4q²

New MR = 400 - 8q

Equating with MC,

400 - 8q = 30

8q = 370

q = 46.25

p = 400 - (4 x 46.25) = 400 - 185 = 215

TR = 215 x 46.25 = 9,943.75

TC = 500 + (30 x 46.25) = 500 + 1,387.5 = 1,887.5

New profit = 9,943.75 - 1,887.5 = 8,056.5

Since profit will increase after campaign, the campaign is beneficial.