Price Theory - Industry Analysis

Industry Analysis

Step 1: Using the information provided in the scenario, derive a profit function for a typical firm in the industry. Use to denote the quantity produced by this firm, and to denote the combined production of the remaining two firms.

Given that:

Fixed Cost (FC) = $400000

Marginal Cost (MC) = $160

· With a constant marginal cost, the total cost function is:

· The given inverse demand function is . Here, is the total output sold in the market, which is the sum of outputs of the three firms in the market. I.e., .

· Therefore, the inverse demand function is: The question has asked to denote output of other firms by .

· Therefore, this allows inverse demand to be written as:

· And ’s firm profit function can be written as:

Step 2: Derive the best-response function for the typical firm.

· The partial derivative of this profit function with respect to is:

· Setting the derivative equal to zero and solving for to find best response function:

Step 3: Find the equilibrium quantity for the typical firm, the equilibrium market quantity, and the equilibrium market price.

· Giving that all firms are identical each firm will produce the same quantity in equilibrium.

· If we replace X with (N – 1) in ’s firm best response function.

· Here N is the number of firm and we have totally 3 firms, therefore N = 3.

· From that we have:

· Therefore, the Nash Equilibrium quantity of three firms is:

· In equilibrium, the total quantity produced by firms in the market is:

· The equilibrium price at this quantity is:

Step 4: Find the equilibrium profit for the typical firm and the equilibrium consumer sur-plus.

· The Profit of typical firms:

· The consumer surplus is the area under the demand curve and above the equilibrium price line:

Step 5: Find the new equilibrium quantities and price for the market. Use to denote the quantity produced by Aggregate Inc., and to denote the quantity produced by the merged firm, BigCon.

Given that Firm B and Firm C is merged, and the MC of these firm now is $145 and the fixed cost now equal to 600000.

Firm ’s best response remains the same as before.

After the merger, the new merged firm takes firm 's quantity as given and solves its profit-maximization problem to arrive at its best response function, . Firm A's best response function remains unchanged. Firm 's best response function from Step 2 was = where X is the quantity produced by other firms. After the merger, the quantity produced by other firms is , the quantity produced by the merged firm. Firm A's best response function is now =

The merged firms, firm’s profit function now is:

· The partial derivative of this profit function with respect to is:

· Setting the derivative equal to zero and solving for to find best response function:

This is the merged firm's best response function.

· Now we have two best response functions with two unknowns: and . Plugging the value of into the equation for will give the optimal output level of the merged firm.

Therefore

· The new market equilibrium quantity is:

· The new market equilibrium price is:

Step 6: Find the new equilibrium firm profits and consumer surplus.

· Firm A’s new equilibrium profit is:

· The merged firm’s new equilibrium profit is:

· Each firm in the merged firm earns a profit of = 122500

· All three firms' profits have increased because of the merger.

· Consumer surplus is:

· Consumer surplus has decreased because of the merger as the merged firm now has greater market power and is able to extract more consumer surplus from the market.