Question

Rock-Steady Ballast Solutions can produce maritime ballast (literal dead weight!) according to the cost function C ( q ) = 5 q, where cost is measured in dollars and q is tons of ballast produced. Rock-Steady's marginal cost of ballast production is therefore M C = 5 dollars per ton. Rock-Steady faces the demand curve q = 35 − p, where q is quantity demanded in tons and p is price per ton in dollars.

A.)

First suppose that Rock-Steady acts as a price taker. Using the rule describing optimal choices of a price taking firm, show that Rock-Steady will supply the quantity q ∗ = 30. Find the equilibrium price p ∗ at this quantity q ∗ = 30, and Rock-Steady's profit at this price and quantity.

B.)

Now suppose instead that Rock-Steady acts as a price-setting monopolist. Using the rule describing the optimal quantity choice of a price-setting firm, show that in this case Rock-Steady will supply the quantity q m = 15. Find the monopoly price p m corresponding to this quantity supplied. What is Rock-Steady's profit as a price-setting monopolist?

C.)Using two graphs, one describing equilibrium when Rock-Steady acts as a price taker, and the other describing equilibrium when Rock-Steady acts as a price setter, illustrate how Rock-Steady's monopoly power affects price, quantity sold, producer surplus, consumer surplus, and total surplus. Briefly discuss.

D.)

What is consumer surplus at the price p ∗ and quantity q ∗ arising when Rock-Steady acts as a price-taker? What is consumer surplus at the price p m and quantity q m arising when Rock-Steady acts as a monopolist? What is the dead-weight loss of monopoly in the ballast market?

[Hint: Remember that since Rock-Steady has no fixed costs of production, producer surplus is the same as profit. You thus don't need to re-calculate producer surplus; you can simply use the profit numbers you found in parts (a) and (b).]

Answer 1

Consumer surplus is given by the area below demand curve and above the price line.

Consumer surplus area is highlighted by yellow in the graphs.

Producer surplus by pink.

And Black area is the dead weight loss.

We see that there is no dead weight loss when the firm is the price Taker. In fact, all the total surplus is the consumer surplus as producer surplus is zero. This is the efficienct equilibrium as there is no DWL.

When firm is aa price maker, it sets a higher price. There is producer surplus as well as a dead weight loss.

Total surplus = producer surplus + consumer surplus.

Total surplus will be LOWER when the firm is a PRICE MAKER.

D) IN THIS PART, WE WILL CALCULATE THE AREA OF THE SHADED PORTIONS.

CONSUMER SURPLUS (PRICE MAKER) = 1/2*30*(35-5)

=1/2*30*30

=450

Producer surplus (price Taker) = 0 (given by profits)

Total Surplus(price Taker) = 450+0= 450

Consumer surplus (price maker) = 1/2*(35-20)*15

=1/2*15*15

=112.5

Producer surplus (price maker) = 225 (as given by profits)

Total surplus (price maker) = 112.5+225 = 337.5

Dead weight loss = 450-337.5= 112.5

Let me know if you have any doubt :)