In some markets, e.g., liquor in Rhode Island, firms are allowed to advertise bu

Question

In some markets, e.g., liquor in Rhode Island, firms are allowed to advertise but are not allowed to mention prices or the existence of a sale. Suppose we have a good with a market demand Q = 100 - P. Suppose that there are two firms, each with the same constant marginal cost: c = 20. Those two firms share the monopoly profit. If firms spend a_1 and a_2 in advertising, then firm l's share is a_1/a_1+a_2 and firm 2's share is a_2/a_1+a_2. If neither firm advertises (a_1 = a_2 = 0), then each firm's share is 1/2. Write down the monopoly profit in this market. What is the profit maximizing price? What is the corresponding profit? Let n be this profit. Suppose both firms advertise: firm l's profit is a_2/a_1+a_2 Pi-a_1 and firm 2's profit is a_2/a_1+a_2 Pi-a_2(with Pi being the profit you found in question a). Firms choose their advertising expenditures in order to maximize their profits. What are the advertising expenditures a_1 and a_2 in equilibrium? What is each firm's profit when both firms advertise? Suppose neither firm advertises. What is each firm's profit? Will firms choose to advertise in equilibrium? Is that a Pareto efficient situation? Explain.

Explanation / Answer

a. Monopoly Profit = P*Q - TC = (100 - Q)*Q - MC*Q =  (100 - Q)*Q - 20*Q

dProfit/dQ = 100 - 2Q - 20

Putting dProfit/dQ = 0

80 - 2Q = 0

Q = 40

P = 100 - Q = 100 -40 = 60

Profit = 60*40 - 20*40 = 1,600

b.

Profit1 = (a1/a1+a2) - a1

differentiating wrt a1

dProfit/da1 = a2/(a1+a2)^2* - 1

Putting

dProfit/da1 = a2/(a1+a2)^2* - 1 = 0

a2/(a1+a2)^2* = 1

a2 = (a1+a2)^2/

Similarly

   Profit2 = (a2/a1+a2) - a2

differentiating wrt a2

dProfit/da2 = a1/(a1+a2)^2* - 1

Putting

dProfit/da1 = a1/(a1+a2)^2* - 1 = 0

a1/(a1+a2)^2* = 1

a1 = (a1+a2)^2/

so,

a1 = a2 = (a1+a2)^2/

Putting = 1,600

So a1 = a2 = 400

So, Profit of firm1 = /2 - a = 1600/2 - 400 = 400

   Profit of firm2 = /2 - a = 1600/2 - 400 = 400

c If neither firm advertises then

  Profit of firm1 =Profit of firm2 = /2 = 1600/2 = 800

d.

Yes , firms will chose to advertize in equilibrium , yes that will be a pareto efficient because in that case one can make one firm better off without making other worse off , i.e increasing one firm's profit without reducing other firm profit.

If you don't understand anything, then comment, I will revert back on the same.

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