Ch 14 Worksheet — Firms in Competitive Markets

Question a

What is the fixed cost (FC) for each taco stand? What is the average total cost (ATC) when q = 2?

Fixed Cost, FC ($)

ATC at q = 2 ($)

Hint Fixed cost is the part of TC that does not depend on q — the constant term. ATC = TC / q. At q = 2, plug into TC = 2q² + 8 first, then divide by 2.

Explanation TC = 2q² + 8. The constant term 8 does not change with output, so FC = $8.

At q = 2: TC = 2(4) + 8 = 8 + 8 = $16. ATC = TC / q = 16 / 2 = $8.

Note that ATC equals $8 here — the same as the fixed cost numerically. This is a coincidence of the specific values; it happens because at q = 2 the variable component 2q²/q = 2q = 4 and the fixed component 8/q = 4 add up to exactly 8.

Question b

What is the break-even price for each taco stand — i.e., the minimum ATC?

Break-even Price ($)

Hint ATC = TC/q = 2q + 8/q. To find the minimum, take d(ATC)/dq = 0. Alternatively, use the rule that at the break-even point, MC = ATC. Set 4q = 2q + 8/q and solve for q, then find P = MC.

Explanation ATC = 2q + 8/q. Taking the derivative: d(ATC)/dq = 2 − 8/q² = 0 ⇒ q² = 4 ⇒ q = 2.

Minimum ATC = 2(2) + 8/2 = 4 + 4 = $8.

Cross-check via MC = ATC: 4q = 2q + 8/q ⇒ 2q² = 8 ⇒ q = 2, and P = MC = 4(2) = $8. The break-even price is $8 — any market price above $8 yields positive profit; below $8 yields a loss.

Question c

What is the shutdown price for each taco stand?

Shutdown Price ($)

Hint The shutdown rule: a firm shuts down in the short run when P < min AVC. AVC = VC/q = 2q²/q = 2q. What is the minimum of 2q for q > 0?

Explanation Variable cost VC = 2q², so AVC = VC/q = 2q.

AVC = 2q is an increasing function starting from 0. As q → 0, AVC → 0. There is no positive minimum — AVC approaches zero continuously.

Therefore the shutdown price is $0. In practical terms, the firm will always cover its variable costs for any positive price, so it never shuts down in the short run based on the AVC rule. Only if price falls to zero (or below) would it shut down.

Question d

If the market price is P = $10, how many tacos does each stand produce? What is the profit per stand?

Quantity per stand, q

Profit per stand ($)

Hint A competitive firm sets P = MC. With MC = 4q and P = 10, solve for q. Then profit = TR − TC = P·q − (2q² + 8).

Explanation Profit-maximizing rule P = MC: 10 = 4q ⇒ q = 2.5.

TR = 10 × 2.5 = $25.
TC = 2(2.5)² + 8 = 2(6.25) + 8 = 12.50 + 8 = $20.50.
Profit = $25 − $20.50 = $4.50.

Since P = $10 > min ATC = $8, the firm earns positive economic profit.

Question e

At P = $10, with each stand earning positive profit, what do we expect to happen in this market over the long run?

Entry — positive profits attract new taco stands to State Street Exit — existing stands are losing money and will leave Neither — the market is already in long-run equilibrium Cannot determine without knowing the number of firms

Hint In a competitive market, economic profits act as a signal. If profit > 0, what happens to the number of firms in the long run?

Explanation Positive economic profit signals that resources earn more here than in their next-best use. New entrepreneurs see an opportunity and enter the market. As new stands open, market supply increases, driving price down. Entry continues until P = min ATC = $8, at which point profit = 0 and the market reaches long-run equilibrium.

Question 1

A firm in a competitive market produces Q = 1,000 units. MC = $15, ATC = $11, and P = $12. The firm's economic profit equals:

−$200 $1,000 $3,000 $4,000

Hint Profit = (P − ATC) × Q. The difference between price and average total cost, multiplied by the number of units, gives total profit. Note that MC is not needed here — it tells you how much to produce, but profit is computed from ATC.

Explanation Profit = (P − ATC) × Q = ($12 − $11) × 1,000 = $1 × 1,000 = $1,000.

Since P > ATC, the firm earns positive economic profit — even though the firm is not at its profit-maximizing quantity (MC ≠ P here, since MC = $15 ≠ $12 = P). The question just asks for the profit at this output level.

Question 2

A competitive firm sells output at $45/unit. At 100 units, ATC = $24.50 and FC = $900. What is the firm's variable cost (VC)?

$9,360.25 $7,500.00 $2,450.00 $1,550.00

Hint TC = ATC × Q. Then VC = TC − FC. Find total cost first, then subtract the fixed cost.

Explanation TC = ATC × Q = $24.50 × 100 = $2,450.
VC = TC − FC = $2,450 − $900 = $1,550.

The price of $45 is a distractor here — it tells you the revenue side, but the question asks only about costs. Note that the firm earns TR = $45 × 100 = $4,500 and profit = TR − TC = $4,500 − $2,450 = $2,050.

Question 3

When new firms enter a perfectly competitive market,

the economic profits of existing firms will continue to be zero entering firms earn zero profit the moment they enter existing firms may see their costs rise if more firms compete for limited inputs prices rise as existing firms raise prices to keep new firms out

Hint Think about an increasing-cost industry. When many new restaurants enter and all compete for the same skilled cooks or prime locations, what happens to the wages or rents those inputs command?

Explanation In an increasing-cost industry, entry drives up the prices of scarce inputs (labor, land, raw materials), raising costs for all firms including incumbents. This shifts cost curves upward.

Option A is wrong — entry drives profits down toward zero, not keeps them at zero. Option B is wrong — new entrants may briefly earn positive profits while adjusting. Option D is wrong — competitive firms are price takers and cannot raise prices strategically.

Question 4

A profit-maximizing firm in a competitive market will produce up to the point where:

price equals average total cost marginal revenue equals marginal cost price equals average variable cost total revenue is maximized

Hint The universal profit-maximizing rule holds for any firm (competitive or not): produce where the revenue from the next unit equals the cost of the next unit. For a competitive firm, MR = P, so this simplifies to P = MC.

Explanation The profit-maximizing rule is MR = MC. For a competitive firm, MR = P (because the firm is a price taker), so the rule becomes P = MC.

Option A (P = ATC) describes the break-even condition, not the profit-maximizing quantity. Option C (P = AVC) describes the shutdown threshold. Option D is wrong because maximizing TR ignores costs entirely.

Question 5

In the short run, a competitive firm should shut down if:

price is less than average total cost price is less than marginal cost price is less than average variable cost total revenue is less than total cost

Hint In the short run, fixed costs are sunk — the firm pays them whether it produces or not. So the relevant comparison is whether revenue covers variable costs. If TR < VC (i.e., P < AVC), producing makes the loss worse than shutting down.

Explanation Short-run shutdown rule: P < min AVC.

If P < AVC, each unit sold fails to cover its own variable cost, making production worse than shutting down (where the firm only loses fixed costs). If P > AVC but P < ATC, the firm operates at a loss but covers variable costs and part of fixed costs — still better than shutdown.

Option A (P < ATC) is the long-run exit rule, not the short-run shutdown rule. Option D (TR < TC) can occur even when the firm should keep operating.

Question 6

In long-run equilibrium in a perfectly competitive market, firms earn:

positive economic profit zero economic profit negative economic profit positive accounting profit but zero economic profit

Hint In the long run, if economic profit > 0, new firms enter and drive price down. If economic profit < 0, firms exit and price rises. Where does this process stop?

Explanation In long-run equilibrium, P = min ATC, so TR = TC, meaning economic profit = 0.

Note that economic profit includes the opportunity cost of the owner's time and capital. Zero economic profit means the owner is earning exactly the market return on their resources — not nothing. Owners still earn a normal accounting profit. Option D is often cited as also true: firms earn positive accounting profit (revenue exceeds explicit costs) but zero economic profit (when implicit costs are included).

Question 7

In a competitive market, the firm's demand curve is horizontal because the firm is a price taker.

Hint A price taker faces a market price it cannot influence. If the firm tries to charge above the market price, what happens to its sales?

Explanation True. A competitive firm is so small relative to the market that it cannot affect the market price. It can sell any quantity it wants at the going price P, but nothing above P. This creates a perfectly horizontal (perfectly elastic) demand curve at the market price. This also means MR = P for the competitive firm.

Question 8

A competitive firm should exit the market in the long run if price is below average variable cost.

Hint There are two different rules: one for the short run (shutdown) and one for the long run (exit). In the long run, all costs are variable — there are no sunk fixed costs. What is the relevant comparison for long-run exit?

Explanation False. The short-run shutdown rule is P < min AVC. The long-run exit rule is P < min ATC.

In the long run, all costs are variable — the firm can avoid fixed costs by exiting. So the relevant threshold is average total cost, not average variable cost. If P < ATC in the long run, the firm does not cover all its costs (including the now-avoidable fixed costs) and should exit.

Question 9

If existing firms in a competitive market are earning positive economic profits, we expect new firms to enter the market in the long run.

Hint Economic profit measures earnings above the next-best opportunity. If a taco stand earns $10,000/year in economic profit, what does that signal to a food truck owner currently earning market returns elsewhere?

Explanation True. Positive economic profit is the entry signal in competitive markets. It means resources employed in this industry earn more than they could elsewhere. Entrepreneurs observe this opportunity and enter, increasing supply, lowering price, and eroding profits until the long-run equilibrium of zero economic profit is restored. This is the self-correcting mechanism that drives competitive markets toward efficiency.

Question 10

A firm's short-run supply curve is its marginal cost curve above the average total cost curve.

Hint A firm produces in the short run as long as it covers its variable costs — not total costs (which include sunk fixed costs). So the MC curve becomes the supply curve once P is above which average cost curve?

Explanation False. The short-run supply curve is the MC curve above the average variable cost (AVC) curve, not the ATC curve.

The shutdown point occurs at P = min AVC. For prices below min AVC, the firm produces nothing (shuts down). For prices above min AVC, the firm produces where P = MC. The portion of MC above AVC is the short-run supply curve. ATC is irrelevant for the shutdown decision in the short run.

Question f

Returning to State Street: in the long run, what will the market price of one taco be? How many taco stands will operate in the market?

Long-run price, P ($)

Number of stands

Hint Long-run equilibrium: P = min ATC = $8 (from Question b). Use market demand P = 100 − 2Q to find total market quantity at P = 8. Each stand produces q = 2 at break-even. Number of stands = total Q ÷ 2.

Explanation In long-run equilibrium, entry drives P down to min ATC. From Question b, min ATC = $8.

Market demand at P = 8: 8 = 100 − 2Q ⇒ 2Q = 92 ⇒ Q = 46 tacos total.

At the break-even price of $8, each stand produces q = 2 (from MC = ATC at q = 2). Number of stands = 46 ÷ 2 = 23 stands.

Each stand earns exactly zero economic profit: TR = $8 × 2 = $16, TC = 2(4) + 8 = $16. Profit = $0.

Practice Worksheet

Short Answer — Taco Stands on State Street

Short Answer — Profit at Market Price

Multiple Choice

True or False

Short Answer — Long-Run Equilibrium