L10: Perfect Competition

Suppose a forestry services firm in a perfectly competitive market has a cost function 𝐶=10+2𝑞+𝑞2, and takes a price of 𝑝=10. (This is the same scenario as in Lecture Exercise 10.4.1, i.e. use your answer for LE10.4.1 as the pre-tax quantity.) What is the change in profits after a $2/unit tax is assessed on the firm?

-7 As solved in LE10.4.1, the pre-tax quantity produced is 4. Total costs were 10+2𝑞+𝑞2=10+2(4)+(4)2=34, and total revenues were 𝑝𝑞=10(4)=40, for a profit of 40−34=6. Now solve the post-tax quantity produced. Differentiate the cost function to get marginal cost: 𝑀𝐶=4+2𝑞. Then set marginal revenue (price) equal to marginal cost: 10=4+2𝑞. So 𝑞=3. Total costs were 10+4𝑞+𝑞2=10+4(3)+(3)2=31, and total revenues were 𝑝𝑞=10(3)=30, for a profit of 30−31=−1. The firm is losing money! (However, notice that it is not losing as much as it would by producing zero units.) The change in profit is −1−6=−7.

Suppose a forestry services firm in a perfectly competitive market has a cost function 𝐶=10+2𝑞+𝑞^2, and takes a price of 𝑝=10. What is the profit-maximizing quantity for the firm to produce?

4. Differentiate the cost function to get marginal cost: 𝑀𝐶=2+2𝑞. Then set marginal revenue (price) equal to marginal cost: 10=2+2𝑞. So 𝑞=4. By inspection (or by a second-order derivative), this is a maximum and not a minimum.

What is necessarily true under perfect competition? A. Firms are price takers on the output side B. Firms are price takers on the input side C. Demand for each firm's output is perfectly inelastic D. Supply for each firm's inputs is perfectly inelastic

A, B Under perfect competition, firms are price takers on both the input and the output side. This means that the demand and supply for each firm's outputs and inputs are perfectly elastic.

What conditions are necessary for demand for a firm's outputs to be perfectly elastic? A. There are low transaction ("shopping") costs B. There is no collusion among firms C. Consumers know all prices D. Firms have no sunk or fixed costs E. Consumers believe that firms sell identical products F. All firms are identical

A, C, E The necessary conditions for perfectly elastic demand are: * Consumers believe that firms sell identical products * Consumers know all prices * There are low transaction ("shopping") costs

In the short run, when should a firm decide to shut down? A. When total cost exceeds total revenue B. When average variable cost exceeds price C. When average cost exceeds marginal revenue D. When fixed cost exceeds total revenue E. When total variable cost exceeds total revenue

B, E. In the short run, a firm should shut down when total variable cost exceeds total revenue, which is also when average variable cost exceeds price. Fixed costs cannot be avoided in the short run, so they are irrelevant to the shutdown decision. (You put B, C).

A firm has total revenues of 14 billion dollars. It spends 5 billion dollars on fixed costs, and spends 7 billion dollars on variable costs. Is the firm making economic profits?

Can't be determined. While we observe that the firm has accounting profits of 2 billion dollars, we do not know the firm's opportunity costs, so we cannot calculate its economic profits.

In the short run, what is the profit maximizing condition for firms in perfectly competitive markets?

In the short run, the profit maximizing condition for firms in perfectly competitive markets is that marginal cost equals price. Observe that in a perfectly competitive market, price is equal to marginal revenue.

The elasticity of demand facing one firm in a perfect competitive market is _____ the market elasticity of demand.

Much larger in magnitude than

What happens to the market supply curve and market demand curve as firms enter the market?

The market supply curve becomes more elastic. The more firms there are, the more quantity is called forth by a price increase. Hence, as firms enter the market, the market supply curve becomes more elastic. Unclear about demand.