Production, cost, and perfect competition

1. THE PRODUCTION FUNCTION: TOTAL, MARGINAL, AVERAGE — AND THE TURN

The production function relates inputs to output. In the short run at least one input — the plant, the ovens, the land — is fixed, and the firm changes output by changing the variable input, usually labor. Three numbers describe what each worker does:

Diminishing marginal returns. As more of the variable input is added to a fixed input, the marginal product eventually falls: the fourth worker has less of the fixed oven to work with than the third did. Marginal product can rise at first — specialization, the division of labor — but the fixed input always wins in the end. The CED’s definition is exactly that sentence: diminishing marginal returns “occur as the firm employs more of one input, holding other inputs constant.”

The two readings that score. Diminishing marginal returns begin with the first worker whose marginal product is lower than the previous worker’s — here the third. And average product rises while marginal product is above it and falls once marginal product drops below it, so the two cross where average product peaks. The average is pulled toward the marginal, always; that is arithmetic, not economics, and it returns in card 2 as the reason marginal cost cuts the average cost curves at their minimums.

2. SHORT-RUN COSTS: SEVEN NUMBERS FROM TWO, AND THE SHAPE THEY MAKE

In the short run a firm pays for the fixed input whether it produces or not — total fixed cost, TFC, constant at every output including zero — and pays for the variable input in proportion to how much it uses — total variable cost, TVC. Everything else is a ratio or a difference:

Why marginal cost is U-shaped. With a wage $w$ per worker, the cost of one more unit is the wage divided by how many units the next worker adds: $\text{MC}=w∕\text{MP}$. When marginal product rises, marginal cost falls; when diminishing returns set in and marginal product falls, marginal cost rises. The CED states the link directly: “production functions with diminishing marginal returns yield an upward-sloping marginal cost curve.”

Table or smooth model? Ferris can choose the whole-worker outputs in its table. Its batch MC need not equal price at the best output; compare total profit at every feasible output, including zero. In a smooth model, an interior optimum on rising MC satisfies MR $=$ MC. The familiar MC-at-minimum-average relationships describe that smooth model; the table shows their discrete counterpart. AVC is minimized at both 24 and 36 here; ATC is minimized at 44.

The three shapes to know by sight. AFC falls forever — the same fixed cost spread over more units. AVC and ATC are U-shaped, and ATC sits above AVC by exactly AFC, so the gap closes as output grows. MC crosses each average curve at its minimum: while the marginal unit costs less than the average, it pulls the average down; once it costs more, it pulls the average up. What shifts them: a change in the wage or in productivity moves MC, AVC and ATC; a change in rent or another fixed cost moves AFC and ATC and leaves MC and AVC alone. Specialization and the division of labor lower marginal cost.

3. LONG-RUN COSTS: EVERY INPUT VARIABLE, AND WHAT SCALE DOES

In the long run “firms can adjust all their inputs, and as a result, all costs become variable.” There is no fixed cost, no AFC, and no diminishing returns in the short-run sense — the firm chooses its plant size along with its labor. The long-run average total cost curve, LRATC, traces the lowest average cost of each output when the plant is chosen freely: the envelope of every short-run ATC curve.

The vocabulary, and what each word measures. Returns to scale describe output when all inputs change together: doubling every input more than doubles output (increasing), doubles it (constant), or less than doubles it (decreasing). Economies of scale describe the LRATC curve: falling as output grows (economies — bulk buying, specialization, spreading design costs), flat (constant returns, the efficient scale), rising (diseconomies — coordination and management strain). The minimum efficient scale, MES, is the smallest output at which LRATC reaches its minimum.

Why the exam cares. MES against the size of the market decides how many firms can fit: an MES that is a large share of market demand leaves room for a few large firms; an MES that is tiny beside the market leaves room for many, which is the perfect competition of card 7. Diminishing returns and diseconomies of scale are different things — one input against a fixed one in the short run, every input together in the long run — and mixing the words is the loss the CED’s note anticipates.

4. TYPES OF PROFIT: THE COST THE ACCOUNTANT DOES NOT SEE

Explicit costs are paid out — wages, rent, materials, interest on a loan. Implicit costs are what the owner’s own resources could have earned elsewhere — the salary given up to run the business, the interest the invested savings would have paid, the return that compensates for risk. Two profits follow:

Which one decides. “Firms respond to economic profit (loss) rather than accounting profit.” An owner earning a $50,000 accounting profit who could earn $65,000 by closing and taking a job is losing $15,000 a year by staying, and in the long run leaves. Normal profit is the accounting profit that just covers the implicit costs — the return the owner needs to stay — and it corresponds to zero economic profit. When card 7 says firms earn zero economic profit in long-run equilibrium, it means they earn exactly a normal profit: enough to stay, not enough to attract anyone else.

5. PROFIT MAXIMIZATION: THE MARGINAL RULE, AND THE RECTANGLE IT PRODUCES

A firm chooses the feasible output with the highest total profit, including zero output. With smooth curves, an interior optimum on rising MC satisfies MR $=$ MC, subject to the shutdown comparison. With Ferris’s table, evaluate each complete output choice: early batches cannot be skipped just because a later batch has lower marginal cost. A falling-then-rising MC schedule makes “stop at the first expensive batch” an unsafe shortcut.

Marginal revenue for a price taker. A perfectly competitive firm sells every unit at the market price, so each unit adds exactly $P$ to revenue: $\text{MR}=P$, a horizontal line at the market price, which is also the demand curve the firm faces. The rule becomes $P=\text{MC}$.

Profit as an area. Once $Q^{\ast }$ is chosen, profit per unit is $P-\text{ATC}$ read at $Q^{\ast }$, and total profit is that height times $Q^{\ast }$: the rectangle between the price line and the ATC curve, from the axis to $Q^{\ast }$. Equivalently $\text{TR}-\text{TC}$. Both give the same number, and the exam accepts either — but the rectangle’s height is ATC at the chosen quantity, never at the curve’s minimum. When price is below ATC the same rectangle is a loss.

6. PRODUCE OR SHUT DOWN; STAY OR EXIT — TWO RUNS, TWO CURVES

A firm can lose money and still be right to keep producing. The short-run question is whether producing loses less than not producing — and not producing still costs the fixed cost.

The shutdown rule. Compare total revenue with total variable cost at the best positive output. If $P>\text{AVC}$ there, operating covers variable cost and contributes toward fixed cost. If the firm makes a loss, that loss is smaller than TFC. If $P<\text{AVC}$, operating loses more than shutting down, so choose zero output. At $P=\min \text{AVC}$, operating and shutting down tie: both lose exactly TFC.

The long-run rule. Once every cost is variable there is no fixed cost to keep paying, and the comparison is price against average total cost. Economic losses — price below minimum ATC — lead firms to exit the market; economic profits lead firms to enter, if nothing bars them. So a price between minimum AVC and minimum ATC is a firm that operates today and leaves eventually. The exam asks “should the firm shut down” and “will firms exit” as different questions, and card 7 draws what the exits do to the price.

7. PERFECT COMPETITION: THE PRICE TAKER, THE LONG RUN, AND WHY IT IS EFFICIENT

A perfectly competitive market has many buyers and sellers of an identical product, with no barriers to entry or exit and no market power: “firms can sell all their outputs at a constant price determined by the market.” The firm is a price taker. Its demand curve is horizontal at the market price, which is also its marginal revenue, and it chooses output where $P=\text{MC}$.

Short run to long run. At $P_1$ the firm earns economic profit (price above ATC). With no barriers, new firms enter, market supply shifts right, and the price falls; entry stops when the price reaches minimum average total cost, where the last firm to enter earns exactly zero economic profit — a normal profit, card 4. Losses run the film backward: exit, supply shifts left, price rises to the same point. In long-run equilibrium, $P=\text{MC}=\text{minimum ATC}$ and economic profit is zero.

Why that is efficient. Allocative efficiency: $P=\text{MC}$ — the price the last buyer paid equals the cost of the last unit made, so the market produces exactly the units worth more to a buyer than they cost to make. Productive efficiency: every firm produces at minimum ATC, the lowest cost per unit its technology allows. Prices in a competitive market “communicate to consumers and producers the magnitude of others’ marginal costs of production and marginal benefits of consumption.” A perfectly competitive market in long-run equilibrium has both efficiencies; Unit 4’s structures each give one or both up.

Cost industries. Whether the long-run price returns to the old level depends on what entry does to costs. In a constant-cost industry input prices do not change with entry and the long-run supply curve is horizontal at minimum ATC. In an increasing-cost industry entry bids up input prices, ATC rises, and long-run supply slopes upward. In a decreasing-cost industry entry lowers input costs and long-run supply slopes downward. The long-run price “depends on the portion of the long-run cost curves on which firms operate.”

8. THE GRAPH THE EXAM SCORES

A correctly labeled perfect-competition diagram is a checklist, and the scorer runs it in this order. Draw in the same order and nothing is forgotten.

1.

Two graphs, side by side, when the market is in the question: the market on the left with price and market quantity, the firm on the right with price, cost and quantity. The price line runs across from one to the other.

2.

Every curve named: $D$ and $S$ on the market; MC, ATC, AVC on the firm; the horizontal line at the market price labeled $P=\text{MR}=D$ (for the firm).

3.

The quantity, dropped to the axis, at the point where MR crosses MC on MC’s rising side.

4.

The rectangle, when profit or loss is asked: from the axis to $Q^{\ast }$, between the price line and ATC at $Q^{\ast }$. Say which it is — profit if price is above ATC, loss if below.

5.

The shift, when the long run is asked: the new supply curve named and arrowed on the market, the new price line drawn across to the firm, and the new quantity dropped.

6.

The words: which decision (produce or shut down; enter or exit) and which curve decided it.

Two habits that cost nothing. Write MC’s label at its top and the averages’ labels at their right ends, so no label sits on a crossing. And draw the price line first, then find $Q^{\ast }$ from it — the order in which the firm itself decides.