A firm in a competitive industry has patented a new process for making widgets. The new process lowers the firm's average costs, meaning this firm alone can earn real economic profits in the long run.

1) If the market price is $20 per widget and the firm's marginal cost curve is given by MC=0.4q, how many widgets will the firm produce?

2) Suppose a government study has found that the firm's new process is polluting the air and estimates the social marginal cost of widget production by this firm to be SMC=0.5q. If he market price is still $20, what is the socially optimal level of production for the firm?

3) What should the amount of a government - imposed excise tax be in order to bring about this optimal level of production?

1) The firm will produce 50 widgets.

In a perfectly competitive industry, the price is said to be equal to the marginal cost. This is because the marginal revenue of the product becomes the price of the product. Marginal cost is the extra cost of producing additional product. Marginal revenue is the additional benefit of the additional product.

To solve this question, we make the price of the product, $20, be equal to marginal cost, 0.4q.

P = MC

20 = 0.4q

Evaluate further by making q the subject of the equation.

q = 20/0.4

q = 50

Therefore, the firm will produce 50 widgets.

2) The social optimal level of production for the firm is 40.

Social marginal cost is the society's impact on the additional production which in turn changes the total cost of the product. Determining the social optimal level of production means that the marginal cost is equal to the marginal benefit.

Again, we equal the price to the social marginal cost.

P = SMC

$20 = 0.5q

Evaluate further by making q the subject of the equation.

q = 20/0.5

q = 40.

Therefore, The social optimal level of production for the firm is 40.

3) The amount of a government - imposed excise tax in order to bring about the optimal level of production is $4.

To get the marginal cost when the production is at optimal level, we substitute the optimal level of production, 40 to the marginal cost equation, MC = 0.4q.

MC = 0.4q

MC = 0.4(40)

MC = $16

Therefore, the marginal cost is $16.

Currently, the price of the product is $20. To reach that price, an excise tax is added with the marginal cost of $16.

excise tax + marginal cost = Price

excise tax = Price - marginal cost

Let us substitute the data of the problem to the equation.

excise tax = $20 - $16

excise tax = $4

Therefore, the excise tax is $4.