Question

The inverse demand curve for steel is P​ = 300−​Q, where price P is dollars per ton and output Q is millions of tons of steel. The industry marginal cost of producing a ton of steel is MC​= 20 ​+ 2Q, which is the industry supply curve. The industry marginal external cost of the damage caused by pollution emitted during the production of one additional ton of steel is MEC ​= 66 ​+ Q. The socially efficient amount of steel to produce is ? million​ tons, and the socially efficient price is ​$ per ton. ​(Enter your responses as real numbers rounded to two decimal​ places.)

Answer 1

The socially efficient amount of steel to produce is 46 million tons, and the socially efficient price is $254 per ton.

Step-by-step explanation:

The socially efficient amount of steel to produce can be determined by finding the intersection of the marginal cost and marginal external cost curves. The industry supply curve represents the marginal cost of producing steel, which is given by MC = 20 + 2Q. The marginal external cost of pollution emitted during production is represented by MEC = 66 + Q.

To find the socially efficient quantity, we need to equate MC and MEC:

20 + 2Q = 66 + Q

Solving this equation, we find Q = 46 million tons.

The socially efficient price can be found by substituting the socially efficient quantity into the inverse demand curve:

P = 300 - Q = 300 - 46 = $254 per ton.