Unit 3

Production, Cost, and the Perfect Competition Model: the one-page sheet

3.1 The Production Function

A production function shows how much output a firm gets from its inputs. In the short run at least one input is fixed, so adding workers eventually brings diminishing marginal returns: each worker adds less than the one before. Marginal product is the change in total product divided by the change in labor, and average product is total product divided by labor. Marginal product above average pulls the average up; below it, the average falls; total product peaks where marginal product reaches zero.

A production function links inputs to output. In the short run at least one input is fixed; in the long run every input can change.
Total product (TP) is all the output. Marginal product: $\text{MP} = \frac{\Delta \text{TP}}{\Delta L}$ . Average product: $\text{average product} = \frac{\text{TP}}{L}$ .
MP often rises at first (specialization), then falls: diminishing marginal returns, from adding a variable input to a fixed one.
When MP is above average product, average product rises; when MP is below average product, average product falls. TP is at its peak where MP is zero.

each new worker has less of the fixed input to work with the marginal product of each new worker falls: diminishing marginal returns average product falls too total product rises more and more slowly and stops rising when marginal product reaches zero

production function: The relationship between the inputs a firm uses and the most output it can make from them. In the short run at least one input is fixed; in the long run every input can change.
total product: Total product (TP): the whole amount of output a firm produces with a given amount of an input, such as a number of workers.
marginal product: Marginal product (MP): the extra output from one more unit of an input, the change in total product divided by the change in that input.
average product: Average product: output per unit of an input, total product divided by the amount of that input (for labor, output per worker).
diminishing marginal returns: Diminishing marginal returns: in the short run, as more of a variable input is added to a fixed input, the marginal product of that input eventually falls.

3.2 Short-Run Production Costs

Short-run costs are fixed (the same at every output, even zero) or variable (rising with output); total cost is their sum. Dividing by output gives AFC, AVC and ATC. Marginal cost is the change in total cost divided by the change in output; diminishing marginal returns make it rise. Because MC pulls an average down when below it and up when above it, MC crosses AVC and ATC at their lowest points. A change in a fixed cost shifts only ATC; a change in a variable cost shifts MC, AVC and ATC.

Total fixed cost (TFC) is the same at every output, even zero. Total variable cost (TVC) rises with output. TC = TFC + TVC.
Averages divide by output: AFC = TFC / Q, AVC = TVC / Q, ATC = TC / Q = AFC + AVC.
Marginal cost: $\text{MC} = \frac{\Delta \text{TC}}{\Delta Q}$ . Divide by the change in output.
MC crosses AVC and ATC at their lowest points. A fixed cost moves ATC (and AFC) only; a variable cost moves MC, AVC and ATC.

the marginal product of labor eventually falls (diminishing marginal returns) each extra unit takes more paid hours to make, so marginal cost rises it pulls each average up, so AVC and ATC turn upward MC crosses AVC and ATC at their lowest points

total fixed cost: Total fixed cost (TFC): a cost that does not change with output in the short run, such as rent, and that is paid even when output is zero.
total variable cost: Total variable cost (TVC): a cost that rises and falls with output, such as materials and hourly labor; it is zero when output is zero.
average total cost: Average costs are costs per unit of output: average fixed cost (AFC = TFC / Q), average variable cost (AVC = TVC / Q) and average total cost (ATC = TC / Q = AFC + AVC).
lump-sum tax: A tax of a fixed amount that does not depend on how much a firm produces (a lump-sum subsidy is a fixed payment). It changes total fixed cost, AFC and ATC, but not marginal cost or AVC.

3.3 Long-Run Production Costs

In the long run every input can change, so a firm chooses the plant size with the lowest cost for each output; long-run average total cost traces those lowest costs. Returns to scale compare the growth of output with the growth of all inputs. With input prices unchanged, increasing returns bring economies of scale (falling LRATC), constant returns a flat LRATC and decreasing returns diseconomies of scale (rising LRATC). Minimum efficient scale, the smallest output at the lowest LRATC, compared with market demand, helps decide how many firms an industry can hold.

In the long run every input can change. LRATC is the lowest average cost of each output when the firm picks the best plant size.
Returns to scale: double every input; if output more than doubles, increasing returns; exactly doubles, constant; less than doubles, decreasing.
LRATC falls with economies of scale, is flat with constant returns to scale and rises with diseconomies of scale.
Minimum efficient scale is the smallest output with the lowest LRATC. Large next to market demand: few firms. Small: many firms.

it can use specialized workers and machines and buy in bulk long-run average total cost falls: economies of scale LRATC hits its lowest level and may stay flat for a range: constant returns to scale costs grow faster than output, so LRATC rises: diseconomies of scale

long-run average total cost: Long-run average total cost (LRATC): the lowest average total cost of producing each output when the firm can change every input, including its plant size.
economies of scale: Economies of scale: long-run average total cost falls as the firm grows. Constant returns to scale: it stays flat. Diseconomies of scale: it rises as the firm grows.
returns to scale: How output responds when every input grows by the same share. If inputs double and output more than doubles, increasing returns to scale; exactly doubles, constant; less than doubles, decreasing returns to scale.
minimum efficient scale: Minimum efficient scale: the smallest output at which long-run average total cost reaches its lowest level.

3.4 Types of Profit

Accounting profit subtracts only explicit costs from total revenue. Economic profit also subtracts implicit costs, the income the owner gives up by using her own time, savings and property in the business, so it is never larger than accounting profit. Zero economic profit is a normal profit: the owner earns what she could earn elsewhere. Positive economic profit means resources earn more here than in their next-best use, which draws in new firms; an economic loss means they earn less.

Accounting profit = total revenue - explicit costs.
Economic profit = total revenue - explicit costs - implicit costs = accounting profit - implicit costs. Below zero it is an economic loss.
Normal profit is zero economic profit: revenue covers every opportunity cost, so the owner does as well as in her next-best choice.
Economic profit, not accounting profit, signals whether resources earn more in an industry than elsewhere.

she gives up the salary and interest they could earn elsewhere: implicit costs economic profit is smaller than accounting profit the business pays more than the owner's best alternative other entrepreneurs are drawn to it

accounting profit: Total revenue minus explicit costs, the money actually paid out to run the business.
economic profit: Total revenue minus explicit and implicit costs (accounting profit minus implicit costs). A negative economic profit is an economic loss.
normal profit: Zero economic profit: revenue just covers every cost, explicit and implicit, so the owner earns exactly what her resources would earn in their next-best use.

3.5 Profit Maximization

Marginal revenue is the change in total revenue from one more unit. A firm maximizes profit by producing where MR = MC: from a table, the last unit whose MR is at least its MC. A firm that sells every unit at a market price it cannot change has MR = AR = P, so its demand curve is a horizontal line, d = MR = AR = P. Profit is TR - TC = (P - ATC) x q at the profit-maximizing output: on a graph, the rectangle from the price down to ATC, out to that output.

Marginal revenue: $\text{MR} = \frac{\Delta \text{TR}}{\Delta Q}$ , the extra revenue from one more unit.
The profit-maximizing rule: produce where MR = MC. From a table: the last unit whose MR is at least its MC.
A firm that sells every unit at one market price has MR = AR = P: its demand curve is horizontal, d = MR = AR = P.
Profit = TR - TC = (P - ATC) x q, at the profit-maximizing q: the rectangle between the price and ATC.

producing it adds MR - MC to profit, so the firm expands the gap between MR and MC shrinks one more unit would add nothing to profit, so profit is at its largest it measures profit as (P - ATC) x q*, the rectangle from the price down to ATC

marginal revenue: Marginal revenue (MR): the extra revenue from selling one more unit, the change in total revenue divided by the change in quantity.
profit-maximizing rule: Produce the output where marginal revenue equals marginal cost (MR = MC); from a table, the last unit whose MR is at least its MC.
firm demand curve: For a firm that sells every unit at one market price, the demand curve is a horizontal line at that price, and it is also the firm's marginal and average revenue: d = MR = AR = P.

3.6 Firms' Short-Run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market

In the short run a firm compares the price with average variable cost: if P is at least the lowest point of AVC it produces where MR = MC, even at a loss, because closing would lose the whole fixed cost; if P is below that point it shuts down. Fixed costs do not change that choice. Above the shutdown point, MC is the firm's short-run supply curve. In the long run, economic profit draws new firms in and losses push firms out; entry shifts market supply right and exit shifts it left, moving the price until economic profit is zero.

Short run, shutdown rule: produce (where MR = MC) if P is at least the lowest point of AVC; shut down if P is below it. Shut down, the loss is the fixed cost.
Fixed costs do not change MC or AVC, so they do not change the short-run output choice.
Above the shutdown point, the MC curve is the firm's short-run supply curve.
Long run: economic profit draws firms in (entry), shifting market supply right; losses push firms out (exit), shifting it left, until economic profit is zero.

firms make economic losses some firms exit the market market supply shifts left and the price rises the remaining firms earn zero economic profit, so exit stops

shutdown rule: In the short run, a firm produces where MR = MC as long as the price is at least the lowest point of average variable cost; below that price (the shutdown point) it shuts down and loses only its fixed cost.
entry and exit: In the long run, positive economic profit draws new firms into a market (entry) and economic losses push firms out (exit), shifting market supply until economic profit is zero.

3.7 Perfect Competition

In perfect competition, many firms sell an identical product and can enter or exit freely, so each firm is a price taker: its demand curve is horizontal at the market price, d = MR = AR = P. Drawn side by side, the market sets the price and the firm produces where MR = MC; profit or loss is (P - ATC) x q. In the long run, profit draws firms in and losses push firms out until the price equals minimum ATC: zero economic profit, P = MC (allocative efficiency) and production at the lowest ATC (productive efficiency). In a constant-cost industry the price returns to the same level, so long-run supply is horizontal.

Perfect competition: many buyers and sellers, identical products, known prices, free entry and exit. Each firm is a price taker.
Draw market and firm side by side: the market price carried across is the firm's horizontal d = MR = AR = P; the firm produces q where MR = MC.
Long-run equilibrium: entry and exit push P to minimum ATC, so economic profit is zero and P = MC = minimum ATC.
That outcome is allocatively efficient (P = MC) and productively efficient (lowest ATC). In a constant-cost industry long-run supply is horizontal.

the market price rises and each firm earns an economic profit at its new MR = MC output new firms enter the market market supply shifts right and the market price falls economic profit is zero, entry stops and the market is back in long-run equilibrium with more firms

perfect competition: A market with many buyers and sellers of an identical product, full information about prices and free entry and exit, so each firm is a price taker that cannot change the market price.
long-run equilibrium: In perfect competition, the state in which entry and exit have pushed the price to minimum ATC, so P = MR = MC = minimum ATC and every firm earns zero economic profit.
constant-cost industry: A constant-cost industry is one whose firms' costs do not change as the industry grows or shrinks, so its long-run supply curve is horizontal at minimum ATC. (Increasing- and decreasing-cost industries, whose costs rise or fall with industry size, are an extension.)
allocative efficiency: Producing the quantity at which price equals marginal cost (P = MC), so the value buyers place on the last unit equals the cost of making it and total surplus is as large as it can be.