Question

BER company and Nord Center are competitors in the market for gadgets. The demand conditions in this market are given by the equation Q=1000-P, and both companies can supply the market with gadgets at a constant marginal cost equal to five dollars (they incur no other costs to run their enterprises).

a. Describe in detail what conditions will give rise to price competition between BER and Nord Center. Given that they compete by choosing prices, what is the equilibrium price and quantity in the market for gadgets?

b. Would the outcome above change if BER (and not Nord Center) instead had a constant marginal cost equal to four dollars rather than five? If so, what is the new equilibrium?

Answer 1

Q=1000-P , MC=5

a) The following assumptions must hold:

• Given the firms are identical and produce identicl products.
• They choose prices simultaneously
• Since their products are perfect substitutes, the firm which charges lower prices gets the whole market

Given that they compete by choosing prices, the equilibrium will be at

P1 = P2= MC =5  

Note: this is the only possible equilibrium because: suppose P1 P2

• If P1 < MC, firm 1 will earn a negative profit ( profit= (P1-MC)*Q). It could earn higher profit by deviating to a higher price like P1=MC, where profits are 0
• If  P1 > MC, both earn positive profits, but firm 2 can capture the whole market by just undercutting firm 1's price by a tiny amount.
• If P1 P2=MC, then there are two subcases:
• when MC= P1<P2, then firm 1 earns zero profit but it could deviate to a price slightly above MC but below P2 and earn positive profits (whole market)
• When P1 = P2= MC, both firms earn zero profits and nobody benefits from any deviation from this price.

Now,  Q=1000-P

Q= 1000-5 = 995

So, P1=P2=5, Q=995, Q1= Q2 = 995/2= 497.5

b) now , MC1 of BER= 4, MC2 of Nord Center=5

Here, the outcome would change due to different marginal costs.

Note ,

• If each charges a price equal to their MC, then, P1=4 , P2=5

Here, firm 1 has lower price so it will get the whole market and firm 2 will get zero profits. But firm 1 here also get zero profits as P=MC=4, clearly firm 1 can deviate to a higher price and get positive profits , so this cannot be an equilibrium.

• We know firm 2 cannot charge below its MC ,i.e P2 MC2=5 , since any price below 5 would lead to negative profits. So, if firm 1 charges slightly below 5, it will get the whole market and earn positive profits.
• Hence, equilibrium price P= 4.99
• Quantity= 1000- 4.99 = 995.01, where Q1=995.01 and Q2= 0