Question

A monopolistic firm currently prices its product at $10 and it is able to sell 1000 units. If it cuts price by 10% sales will go up to 1200 units. Marginal cost (MC) is $5.

a. How will the break-even point change?

b. Is it worth cutting price? (i.e., is profit greater)

Answer 1

Consider the given problem here the as “P” decreases from “10” to “9” the “q” increases to “1200” from “1000”, => the demand curve is given by, “P = 15 - 0.05*q”. Now, the marginal cost function is given by, “MC = $5”. So, the break-even point is “P=MC”, => 15 – 0.05*q = 5”.

=> q = 10/0.05 = 2,000”, => the break-even point is given by “P=5, q=2,000”.

So, here at this point the profit is “0”, and this point will not change.

B).

Now, given the demand curve the MR is given by, “MR = 15 – 2*0.005*q”.

=> MR = 15 - 0.01*q”, => at the equilibrium “MR=MC”.

=> 15 - 0.01*q = 5, => q = 10/0.01 = 1000, => q=1000 and P=10”. So, the initial “P” was the profit maximizing price, => as “P” decrease from “10” the level of “P” also decreases. So, it’s not worth cutting price.