Econ unit 3

Time horizon distinguishing the short run from the long run in production

The short run is a period where at least one input is fixed (typically capital or plant size), whereas the long run is a period where all inputs are variable.

Total Product ($TP$)

The overall quantity of output produced by a firm using a given combination of fixed and variable inputs.

Formula for Marginal Product of labor ($MP_L$)

$MP_L = \frac{\Delta TP}{\Delta L}$, measuring the additional output generated by adding one more worker.

Formula for Average Product of labor ($AP_L$)

$AP_L = \frac{TP}{L}$, measuring the output produced per unit of variable input (worker).

The Law of Diminishing Marginal Returns

As successive units of a variable input are added to a fixed input, the additional output produced by each additional unit of the variable input will eventually decline.

Primary economic cause of diminishing marginal returns in the short run

Fixed capital resources (such as equipment or physical workspace) become overcrowded as more variable workers are hired.

Behavior of Total Product ($TP$) when Marginal Product ($MP$) is positive but falling

Total Product increases at a decreasing rate.

Relationship between Marginal Product and Total Product at the peak of $TP$

Marginal Product equals zero ($MP = 0$) when Total Product reaches its maximum.

Intersection point between the Marginal Product ($MP$) curve and Average Product ($AP$) curve

Marginal Product intersects Average Product from above at the exact maximum point of the Average Product curve.

Stage I of production

The range of variable input use where Average Product is increasing, ending where Marginal Product intersects Average Product at its maximum.

Stage II of production

The rational operating range where both Marginal Product and Average Product are declining, but Marginal Product remains positive ($MP \ge 0$).

Stage III of production

The range of variable input use where Marginal Product becomes negative ($MP < 0$) and Total Product is falling.

Calculation: A bakery employs 2 bakers to produce 16 cakes per day, and hiring a 3rd baker increases output to 25 cakes per day. What is the Marginal Product of the 3rd baker?

Using $MP = \frac{\Delta TP}{\Delta L}$, $MP = \frac{25 - 16}{3 - 2} = \frac{9}{1} = 9$ cakes.

Graphical identification: Inflection point on the Total Product ($TP$) curve

The point where the slope of $TP$ stops increasing and begins flattening out, which corresponds precisely to the maximum point on the Marginal Product ($MP$) curve.

Fixed Costs ($FC$)

Expenses that do not change with the quantity of output produced in the short run, even if output is zero (e.g., rent, insurance, factory lease).

Variable Costs ($VC$)

Expenses that change directly with the quantity of output produced (e.g., raw materials, hourly labor).

Formula for Total Cost ($TC$)

$$TC = FC + VC$$

Formula for Average Fixed Cost ($AFC$) and its graphical behavior as output expands

$AFC = \frac{FC}{Q}$; it continuously declines asymptotically toward zero because a constant numerator is divided by an ever-larger quantity.

Why the vertical gap between $ATC$ and $AVC$ shrinks as output increases

The vertical distance equals Average Fixed Cost ($AFC = ATC - AVC$), which decreases continuously as output increases.

Formula for Average Variable Cost ($AVC$)

$$AVC = \frac{VC}{Q}$$

Formula for Average Total Cost ($ATC$)

$ATC = \frac{TC}{Q}$ or $ATC = AFC + AVC$

Formula for Marginal Cost ($MC$)

$$MC = \frac{\Delta TC}{\Delta Q} = \frac{\Delta VC}{\Delta Q}$$

Reason the short-run Marginal Cost ($MC$) curve is U-shaped

It initially declines due to increasing marginal returns from labor specialization, and then increases due to the Law of Diminishing Marginal Returns.

Exact intersection points of the Marginal Cost ($MC$) curve with average cost curves

$MC$ intersects both Average Variable Cost ($AVC$) and Average Total Cost ($ATC$) at their respective minimum points.

Mathematical connection between Marginal Cost ($MC$) and Marginal Product ($MP$)

$MC = \frac{W}{MP_L}$, where $W$ is the wage; thus, when $MP_L$ is at its maximum, $MC$ is at its minimum.

Mathematical connection between Average Variable Cost ($AVC$) and Average Product ($AP$)

$AVC = \frac{W}{AP_L}$, where $W$ is the wage; thus, when $AP_L$ is maximized, $AVC$ is minimized.

Effect of an increase in a lump-sum fixed cost on $MC$, $AVC$, and $ATC$

Marginal Cost ($MC$) and Average Variable Cost ($AVC$) are unaffected; Average Total Cost ($ATC$) shifts upward.

Effect of an increase in a per-unit variable cost (e.g., per-unit tax) on $MC$, $AVC$, and $ATC$

Marginal Cost ($MC$), Average Variable Cost ($AVC$), and Average Total Cost ($ATC$) all shift upward.

Calculation: A firm has $TC = \$120$ at $Q = 0$ and $TC = \$320$ at $Q = 5$. Find $FC$, $VC$, and $ATC$ at $Q = 5$.

Since $TC(0) = FC$, $FC = \$120$. At $Q = 5$, $VC = TC - FC = 320 - 120 = \$200$, and $ATC = \frac{TC}{Q} = \frac{320}{5} = \$64$.

Calculation: Total Cost is $\$140$ when producing 4 units and $\$175$ when producing 5 units. What is the Marginal Cost of the 5th unit?

Using $MC = \frac{\Delta TC}{\Delta Q}$, $MC = \frac{175 - 140}{5 - 4} = \frac{35}{1} = \$35$.

Defining structural characteristic of a firm's long-run production environment

There are no fixed costs or fixed inputs; all resources and costs are completely variable, and firms can freely enter or exit the industry.

Derivation and meaning of the Long-Run Average Total Cost ($LRATC$) curve

The planning envelope curve formed by the lower boundary of all possible short-run Average Total Cost ($SRATC$) curves representing different plant sizes.

Economies of scale

The property whereby Long-Run Average Total Cost ($LRATC$) decreases as output increases in the long run.

Two major operational causes of economies of scale

Labor and managerial specialization, and mass-production technologies or bulk purchasing discounts that lower average cost.

Constant returns to scale

The range of output where Long-Run Average Total Cost ($LRATC$) remains unchanged as output increases.

Diseconomies of scale

The property whereby Long-Run Average Total Cost ($LRATC$) increases as output increases in the long run.

Primary organizational cause of diseconomies of scale

Coordination and communication difficulties, bureaucratic inefficiencies, and worker alienation in very large organizations.

Minimum Efficient Scale ($MES$)

The lowest level of output at which a firm can minimize its Long-Run Average Total Cost.

Conceptual difference between diminishing marginal returns and diseconomies of scale

Diminishing returns is a short-run concept caused by overcrowding a fixed input; diseconomies of scale is a long-run concept where all inputs are increased.

Graphical region of economies of scale on a standard U-shaped $LRATC$ curve

The downward-sloping segment of the $LRATC$ curve where output is increasing.

Explicit costs

Direct monetary out-of-pocket payments made by a firm to purchase or hire resources (e.g., wages, rent, raw materials).

Implicit costs

The forgone monetary value of the next-best alternatives when a firm uses its own self-owned resources without direct cash outlay (e.g., forgone salary, forgone interest on savings).

Formula for Accounting Profit

$$\text{Accounting Profit} = \text{Total Revenue} - \text{Explicit Costs}$$

Formula for Economic Profit

$$\text{Economic Profit} = \text{Total Revenue} - (\text{Explicit Costs} + \text{Implicit Costs})$$

Mathematical comparison between accounting profit and economic profit when implicit costs are positive

Accounting profit is strictly greater than economic profit by the exact amount of the implicit costs.

Normal profit

A condition where economic profit equals zero ($\text{Economic Profit} = 0$), meaning total revenue covers all explicit and implicit opportunity costs, keeping the entrepreneur in business.

Economic meaning of earning a negative economic profit (economic loss)

The firm's resources could earn a higher return in their next-best alternative use.

Calculation: An engineer leaves a $\$70{,}000$ annual job to open a consultancy. In year one, revenue is $\$180{,}000$ and operating costs are $\$60{,}000$. Calculate accounting and economic profit.

$\text{Accounting Profit} = 180{,}000 - 60{,}000 = \$120{,}000$. $\text{Economic Profit} = 180{,}000 - (60{,}000 + 70{,}000) = \$50{,}000$.

Opportunity cost of financial capital invested in a business

The return or interest that could have been earned if the funds were invested in the next-best financial asset instead.

Marginal Revenue ($MR$) formula and definition

$MR = \frac{\Delta TR}{\Delta Q}$, measuring the change in total revenue resulting from selling one additional unit of output.

The universal profit-maximizing rule for all firms

Produce the output level where Marginal Revenue equals Marginal Cost ($MR = MC$), provided price covers minimum average variable cost in the short run.

Firm output decision when $MR > MC$

Increase production, because producing additional units adds more to revenue than to cost, increasing total profit.

Firm output decision when $MR < MC$

Decrease production, because the last unit produced added more to cost than to revenue, reducing total profit.

Per-unit formula for Total Economic Profit or Loss

$$\text{Profit} = (P - ATC) \times Q$$

Total Revenue-Total Cost ($TR - TC$) approach to profit maximization

Profit is maximized at the output quantity where the positive vertical distance between the Total Revenue curve and Total Cost curve is greatest.

Graphical identification: Profit-maximizing quantity on a standard $MR$ and $MC$ graph

Find the point where the $MC$ curve intersects the $MR$ curve from below, then project straight down to the horizontal axis to identify output ($Q^*$).

Calculation: A firm produces at $MR = MC = \$14$. At this quantity, $Q = 80$, price is $\$14$, and $ATC = \$10$. Calculate the firm's total economic profit.

Using $\text{Profit} = (P - ATC) \times Q$, $\text{Profit} = (14 - 10) \times 80 = 4 \times 80 = \$320$.

Identifying profit-maximizing output from a table of discrete values when $MR$ never exactly equals $MC$

Produce the highest output level where $MR > MC$ before $MC$ exceeds $MR$.

The Short-Run Shutdown Rule

A firm should shut down immediately if the market price falls below minimum Average Variable Cost ($P < \text{minimum } AVC$), or equivalently if $TR < VC$.

Economic rationale for a firm operating at an economic loss in the short run when $AVC \le P < ATC$

The price is high enough to cover all variable costs and a portion of fixed costs, resulting in a smaller loss than shutting down completely.

The size of a firm's economic loss if it shuts down operations in the short run

The firm loses an amount exactly equal to its Total Fixed Cost ($\text{Loss} = FC$).

A competitive firm's short-run supply curve

The portion of the firm's Marginal Cost ($MC$) curve that lies above its minimum Average Variable Cost ($AVC$) curve.

Long-run entry condition for prospective firms in a competitive market

Firms enter when market price is greater than Average Total Cost ($P > ATC$), generating positive economic profits.

Long-run exit condition for existing firms in a competitive market

Firms exit when market price is less than Average Total Cost ($P < ATC$), generating persistent economic losses.

Long-run equilibrium condition for a perfectly competitive firm

$P = MR = MC = \text{minimum } ATC$, resulting in zero economic profit (normal profit).

Long-run market adjustment process when existing competitive firms earn short-run economic profits

New firms enter the industry, shifting market supply rightward, driving market price down until $P = \text{minimum } ATC$ and economic profit equals zero.

Long-run market adjustment process when existing competitive firms incur short-run economic losses

Existing firms exit the industry, shifting market supply leftward, driving market price up until $P = \text{minimum } ATC$ and economic profit equals zero.

Calculation: A firm faces price $P = \$7$. At output $Q = 50$, $ATC = \$9$ and $AVC = \$6$. Should the firm produce or shut down in the short run, and what is its profit/loss?

Since $P > AVC$ ($\$7 > \$6$), the firm produces. $\text{Profit} = (P - ATC) \times Q = (7 - 9) \times 50 = -\$100$ (a loss of $\$100$, which is less than its $FC$ of $\$150$).

Calculation: If market price drops to $P = \$3$ while a firm's minimum $AVC = \$4$ and $FC = \$200$, what should the firm do and what is its loss?

The firm should shut down immediately because $P < AVC$. Its short-run loss equals its fixed costs of $\$200$.

Four primary characteristics of a perfectly competitive market structure

A very large number of small firms, identical (standardized) products, no barriers to entry or exit, and firms are price takers.

Why an individual firm in perfect competition cannot influence the market price

Each firm produces a negligible fraction of the total industry output, so altering its production has no discernible effect on market supply.

Shape and price elasticity of demand faced by an individual perfectly competitive firm

A perfectly horizontal (infinitely elastic) demand curve at the prevailing market equilibrium price.

The equality acronym 'Mr. DARP' in perfect competition

For a price-taking firm, Marginal Revenue equals Demand, which equals Average Revenue, which equals Price ($MR = D = AR = P$).

Graphical linkage between the competitive market and the individual firm ('side-by-side' graphs)

The market supply and market demand curves intersect to establish the equilibrium market price, which is extended horizontally to become the firm's horizontal demand curve.

Graphical identification: Area representing total economic profit for a competitive firm

A rectangle with a base extending from 0 to $Q^*$ and a vertical height extending from $ATC$ up to $P$ (where $P > ATC$ at $Q^*$).

Graphical identification: Area representing total economic loss for a competitive firm

A rectangle with a base extending from 0 to $Q^*$ and a vertical height extending from $P$ up to $ATC$ (where $P < ATC$ at $Q^*$).

Productive efficiency condition and definition

Producing goods at the lowest possible per-unit cost, achieved where $P = \text{minimum } ATC$.

Allocative efficiency condition and definition

Producing the optimal mix of goods most desired by society, achieved where Marginal Benefit equals Marginal Cost ($P = MC$).

Efficiency status of a perfectly competitive firm in long-run equilibrium

The firm simultaneously achieves both productive efficiency ($P = \text{minimum } ATC$) and allocative efficiency ($P = MC$).

Long-run industry supply curve in a constant-cost industry

A perfectly horizontal line at the minimum $ATC$ because firm entry and exit do not change input prices.

Long-run industry supply curve in an increasing-cost industry

An upward-sloping curve because the entry of new firms increases industry demand for scarce inputs, bidding up resource costs and shifting each firm's cost curves upward.

Long-run impact of a permanent increase in demand in a constant-cost competitive industry

Market price temporarily rises, inducing entry; long-run market output increases, but the market price returns to its original equilibrium level.

Differential effect of a per-unit subsidy versus a lump-sum subsidy on a firm's short-run output

A per-unit subsidy lowers $MC$, causing the profit-maximizing output ($Q^*$) to increase; a lump-sum subsidy lowers only $ATC$, leaving $MC$ and output unchanged.