A competitive firm has the following short-run cost...

A competitive firm has the following short-run cost function: $C(q)=q^{3}-8 q^{2}+30 q+5$ a. Find $\mathrm{MC}, \mathrm{AC}$, and $\mathrm{AVC}$ and sketch them on a graph. b. At what range of prices will the firm supply zero output? c. Identify the firm's supply curve on your graph. d. At what price would the firm supply exactly 6

A competitive firm has the following short-run cost function: $C(q)=q^{3}-8 q^{2}+30 q+5$
a. Find $\mathrm{MC}, \mathrm{AC}$, and $\mathrm{AVC}$ and sketch them on a graph.
b. At what range of prices will the firm supply zero output?
c. Identify the firm's supply curve on your graph.
d. At what price would the firm supply exactly 6

Key Concepts

Shutdown Rule

The shutdown rule is a criterion used by firms to decide whether to continue operating or shut down in the short run. If the market price is below the firm's average variable cost at the profit-maximizing output level, the firm minimizes its losses by ceasing production, as it cannot cover its variable costs regardless of fixed cost considerations.

Average Variable Cost (AVC)

Average variable cost is obtained by dividing the variable portion of the total cost by the quantity of output produced. This measure is key to determining the minimum price at which a firm should operate in the short run. The AVC is critical for the shutdown decision, as firms will typically cease production if the market price falls below the minimum AVC.

Competitive Firm Supply Decision

In a perfectly competitive market, a firm maximizes profit by producing the quantity at which the market price equals its marginal cost, given that the price is above the average variable cost. This decision-making process encapsulates elements such as the profit maximization condition and the shutdown rule, guiding firms on when to produce or temporarily halt operations.

Average Cost (AC)

Average cost is calculated by dividing the total cost by the quantity of output produced. It reflects the cost per unit of output and helps in assessing the overall efficiency of the production process. Understanding AC is important for analyzing economies of scale and for making pricing decisions in the long run.

Marginal Cost (MC)

Marginal cost represents the additional cost incurred by producing one more unit of output. It is derived by taking the derivative of the total cost function with respect to quantity. This concept is fundamental in determining the optimal output level in profit maximization, as firms typically produce up to the point where the marginal cost equals the market price in a competitive environment.

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