Economics 41 - Elasticity, Production & Costs, Market Structure, Profit Maximisation & Shutdown

Elasticity of Demand

5.1 General definition of elasticity of demand
- A measure of the sensitivity or responsiveness of quantity demanded to changes in the price of the good itself, income, or the price of other goods.
- Three types of demand elasticities:
- 1) Price elasticity of demand (PED)
- 2) Income elasticity of demand (YED)
- 3) Cross price elasticity of demand (XPED)
5.2 Price Elasticity of Demand (PED)
- Definition: A measure of the responsiveness of quantity demanded to a change in its own price. PED looks at a movement along a given demand curve.
- Mid-point formula (the preferred method):
- $Ed = \frac{\frac{Q{new}-Q{old}}{(Q{new}+Q{old})/2}}{\frac{P{new}-P{old}}{(P{new}+P_{old})/2}}$
- Where $Q{new}$ and $Q{old}$ are new/old quantities demanded, and $P{new}$ and $P{old}$ are new/old prices.
- PED is always negative due to the law of demand (price and quantity demanded move in opposite directions). To simplify interpretation, economists use its absolute value: $|E_d|$ .
- Difference between simple vs mid-point formulas:
- Simple formula: $PEd = \frac{\frac{ riangle Q}{Q}}{\frac{ riangle P}{P}}$
- The simple formula can yield different answers for the same movement depending on the base (A→B vs B→A) because it uses different bases.
- Mid-point/base-free method fixes this by using averages in the denominator.
- Example (concert tickets, price moves from $25 to $30; quantity moves from 20,000 to 10,000):
- Using the mid-point formula:
 - Q{old}=20{,}000, ess{Q}{new}=10{,}000,
 P{old}=25, P{new}=30
 - Numerator (quantity change): $\frac{Q{new}-Q{old}}{(Q{new}+Q{old})/2}=\frac{10{,}000-20{,}000}{(10{,}000+20{,}000)/2}=\frac{-10{,}000}{15{,}000}=-0.6667$
 - Denominator (price change): $\frac{P{new}-P{old}}{(P{new}+P{old})/2}=\frac{30-25}{(30+25)/2}=\frac{5}{27.5}=0.1818$
 - PED: $E_d=\frac{-0.6667}{0.1818}\approx -3.67$
 - Magnitude: $|E_d|\approx 3.67$ (Elastic, since >1)
- For the reverse movement (B→A), the magnitude remains the same with the midpoint approach (still ~3.67).
- PED categories (coefficients can range from 0 to ∞):
- Elastic demand: |E_d|>1
- Inelastic demand: |E_d|<1
- Unitary elastic demand: $|E_d|=1$
- Perfectly elastic demand: $|E_d|=\infty$
- Perfectly inelastic demand: $|E_d|=0$
5.2.1 Coefficients of price elasticity of demand (summary)
- Elastic: PED > 1 (percent change in quantity demanded exceeds percent change in price)
- Inelastic: PED < 1 (quantity changes less than price)
- Unitary: PED = 1 (proportional changes)
- Perfectly elastic: PED = ∞
- Perfectly inelastic: PED = 0
5.2.2 Usefulness of Price Elasticity of Demand (and total revenue implications)
- Total Revenue (TR) is the total dollars earned from selling a good or service:
- $TR = P imes Q$
- Relationship between PED and TR depends on elasticity:
- If demand is price elastic (PED > 1): a decrease in price leads to a more-than-proportional increase in quantity, so TR rises. Conversely, a price increase lowers TR.
- If demand is price inelastic (PED < 1): a price decrease raises quantity, but not enough to offset the fall in price, so TR falls; a price increase raises TR.
- If demand is unit elastic (PED = 1): TR remains unchanged when price changes (price and quantity change in perfect proportion).
- Summary of TR behavior with price changes:
- Elastic demand: TR rises when price falls; TR falls when price rises.
- Inelastic demand: TR rises when price rises; TR falls when price falls.
- Unit elastic demand: TR unchanged when price changes.
5.2.3 Determinants of Price Elasticity of Demand
- Availability of substitutes: More/substitutes that are closer, more elastic the demand. Narrow definitions (e.g., a specific brand) yield more substitutes and higher elasticity; broader definitions yield fewer substitutes and lower elasticity.
- Share of budget spent on the product: Small-budget items tend to be price inelastic; large-budget items tend to be price elastic.
- Time: With more time, consumers can substitute more easily; demand becomes more elastic over time.
- Luxury vs. Necessity: Luxuries are more price elastic; necessities are more price inelastic.
- Examples:
- Tobacco may have inelastic demand due to addiction; salt has inelastic demand (low price, small budget share).
- Laptop demand: broader market (e.g., laptops) may be inelastic, but specific brands (Apple, Dell, etc.) are more elastic due to brand substitution.
5.3 Income Elasticity of Demand (YED)
- Definition: Measures the responsiveness of quantity demanded to a change in income.
- Formula (simple, not midpoint):
- $Y{Ed}=\frac{\frac{Q{new}-Q{old}}{Q{old}}}{\frac{Y{new}-Y{old}}{Y_{old}}}$
- 5.3.1 Coefficients of income elasticity of demand
- Negative YEd: occurs when income and quantity demanded move in opposite directions → inferior good.
- Positive YEd: occurs when both income and quantity demanded change in the same direction → normal good.
- Normal goods subdivide into:
 - Luxuries: Y_{Ed} > 1 (income elastic)
 - Necessities: 0 < Y_{Ed} < 1 (income inelastic)
- Usefulness: Helps predict sales with income changes. Example: if income increases by 5% and the YEd for a good is 1.5, then the expected change in quantity is approximately 1.5 imes 5\ ext{%} = 7.5\% increase in quantity.
5.4 Cross Price Elasticity of Demand (XP Ed)
- Definition: Measures the responsiveness of the demand for one good to a change in the price of another related good.
- Formula (simple):
- $XP ext{ Ed} = \frac{\frac{QA^{new}-QA^{old}}{QA^{old}}}{\frac{PB^{new}-PB^{old}}{PB^{old}}}$
- Coefficients of cross price elasticity
- Positive XP Ed: goods A and B are substitutes in consumption.
- Negative XP Ed: goods A and B are complements in consumption.
- Zero XP Ed: goods are unrelated.

Production and Costs

6.1 Decision time frames
- Short run (SR): at least one fixed input; some inputs cannot be changed in the period under consideration.
- Long run (LR): all inputs are variable; there are no fixed inputs.
- Key SR features: two types of inputs:
- Variable input: quantity can be changed during the period (e.g., workers).
- Fixed input: quantity cannot be changed during the period (e.g., plant size).
- Key LR feature: no fixed input; the firm can adjust all inputs (including factory size).
6.2 Short Run Production
- Three main SR product curves: Total Product (TP), Average Product (AP), and Marginal Product (MP).
- Total Product (TP): output produced when additional units of variable input (VI) are added to the fixed input (FI).
- Marginal Product (MP): the change in total output from adding one more unit of VI.
- Formula: $MP = \frac{ riangle TP}{ riangle VI}$
- MP is the slope of the TP curve (the gradient of the tangent at any point).
- Shape of TP and MP:
- MP typically rises at first (increasing returns to a point), then falls (diminishing returns), leading TP to eventually peak and then fall if MP becomes negative.
- Example interpretation: with labor input from 1 to 2 workers, MP rose from 10 to 12 bushels/day; 3–6 workers MP falls; maximum TP occurs at 6 workers; subsequent workers reduce total output (MP negative).
- Average Product (AP): output per unit of VI;
- Formula: $AP = \frac{TP}{VI}$
- Relationship between MP and AP:
- Both curves have the same general shape, but they do not perfectly overlap.
- When MP > AP, AP rises; when MP < AP, AP falls; MP and AP are equal when AP is at its maximum.
- Notation: AP, MP, VI, and TP relationships: MP pulls AP up when MP > AP and pulls AP down when MP < AP.
6.3 Short Run Cost Curves
- In SR, firms incur both fixed costs and variable costs.
- (6.3.1) Total Fixed Costs (TFC): costs of fixed inputs; TFC is a horizontal (flat) line; can shift with changes in fixed inputs (e.g., plant size).
- (6.3.1) Total Variable Costs (TVC): costs of variable inputs; zero when output is zero; increase with output; TVC starts at zero (origin).
- (6.3.1) Total Cost (TC): TC = TFC + TVC; at zero output, TC = TFC; the vertical gap between TC and TVC equals TFC.
- (6.3.2) Short Run Average Cost Curves
- AFC = TFC / Q
- AVC = TVC / Q
- ATC = TC / Q = AFC + AVC
- Shape: typically U-shaped due to AFC consistently falling with output while AVC first falls then rises.
- (6.3.3) Relationship between average and marginal costs
- MC = change in TC when one more unit is produced: $MC = \frac{ riangle TC}{ riangle Q}$
- The MC curve is closely related to the MP curve (mirror image in many contexts): as MP rises, MC falls; as MP falls, MC rises.
- Key points:
 - If MC < AVC or MC < ATC, then AVC or ATC are falling.
 - If MC > AVC or MC > ATC, then AVC or ATC are rising.
 - MC intersects AVC and ATC at their minimum points.
 - Note: MC is not directly related to AFC.
6.4 Production in the Long Run (LR)
- No fixed costs in the LR; all inputs are variable.
- The LR framework allows the firm to choose the best input combination (factor proportions).
- Returns to scale (concept in LR): what happens to output when all inputs are changed proportionately.
- 6.4.1 Long Run Average Cost Curve (LRAC)
- Increasing returns to scale (Economies of Scale): initially, output increases more than proportionately with input increases; LRAC falls.
  - Mechanism: specialization, division of labor, more efficient resource use as the firm expands.
- Decreasing returns to scale ( Diseconomies of Scale): after a point, output grows less than proportionately; LRAC rises.
- Constant returns to scale: output increases proportionately with inputs; LRAC remains constant.

Market Structure

7.1 Firm vs Industry
- Firm: an organization that produces goods/services.
- Industry: a group of firms selling a well-defined product or closely related products.
7.2 Meaning of Market Structure
- A classification system for the key characteristics of a market, including three main determinants of market power:
- The number of firms
- The type of product sold (homogeneous vs differentiated)
- Barriers to entry/exit
7.3 Characteristics of Perfect Competition (PC)
- Large number of small firms; none can influence the market price.
- Homogeneous product; buyers are indifferent among sellers.
- No barriers to entry/exit; firms earn normal profit in the long run.
- PC firm is a price taker with a horizontal (perfectly elastic) demand curve.
- Real-world examples close to PC: some agricultural markets, stock/foreign exchange markets (though perfect competition is an abstraction).
7.4 Monopoly
- A single firm monopolizes the market (e.g., Singapore Post in its industry context).
- Selling a unique product; very strong barriers to entry.
- Monopolist faces the market demand curve (downward sloping) and is a price maker.
- Market power is greater with more inelastic demand.
7.5 Monopolistic Competition
- Many small firms; differentiated products; some market power due to product differentiation.
- Low barriers to entry/exit; SR profits possible but LR profits tend to normal profit due to entry.
- Demand curve for a monopolistically competitive firm is downward sloping and relatively elastic due to close substitutes.
- Firms engage in non-price competition (e.g., packaging, advertising, branding) to create perceived differences and loyalty.
7.6 Oligopoly
- A few large firms dominate the market; mutual interdependence (firms must consider rivals’ reactions).
- Products can be homogeneous (oil, basic metals) or differentiated (cars, bread).
- Barriers to entry are strong, enabling long-run profits.
- Demand in oligopoly can be represented by kinked demand curves due to interdependence, implying price stability in some ranges.
- Firms often compete via non-price competition (advertising, branding, product differentiation).
Profit types across structures
- Economic (supernormal) profit
- Normal profit (zero economic profit)
- Economic loss
Quick comparative notes
- PC: many firms, identical products, free entry/exit, price takers
- Monopoly: one firm, unique product, strong barriers, price maker
- Monopolistic Competition: many firms, differentiated products, free entry/exit, some market power
- Oligopoly: a few firms, either homogeneous or differentiated products, strong barriers, mutual interdependence

Profit Maximisation and Shutdown Condition

8.1 Profit measures: TR, AR, MR
- Total Revenue (TR): the total receipts from selling output.
- Average Revenue (AR): revenue per unit of output; AR = TR / Q.
- Marginal Revenue (MR): the addition to total revenue from selling one more unit; MR = ΔTR / ΔQ.
- For a price taker, MR = P since each additional unit is sold at the same price.
8.2 Profit Maximisation Rule
- The goal is to maximise profit: Profit = TR − TC.
- Two common methods to determine the profit-maximising quantity (Q):
- Method 1 (TR − TC): profit is maximised where TR − TC is at its maximum.
- Method 2 (MR = MC): profit-maximising output occurs where the additional revenue from selling one more unit equals the additional cost of producing that unit.
8.3 Continuation vs shutdown (short run)
- Determine whether to produce or to shut down by comparing price to costs.
- Key relationships:
- TR = P × Q
- TC = ATC × Q = TFC + TVC
- Profit/Loss = TR − TC
- Decision rules (based on price, TR, TVC, and AVC):
- If TR > TVC (or P × Q > TVC), continue production (even if there is a loss, as long as total loss is less than fixed costs).
- If TR ≤ TVC, shutdown in the short run (to minimize losses).
- Shutdown point occurs where P = AVC (i.e., price covers average variable cost).
- Example scenarios (illustrative values):
- Scenario 1: Do not open shop (shutdown) → loss equals TFC (e.g., $100).
- Scenario 2 (P > AVC): Produce; TR = P × Q, TVC known, TFC known; Profit = TR − TC (may be positive).
- Scenario 3 (P < AVC): Do not produce;shutdown; loss equals TFC (since TVC cannot be covered).
- A simplified decision table (typical SR outcomes):
- TR > TC (P > ATC): Economic profit
- TR = TC (P = ATC): Normal profit
- TR < TC (P < ATC): Economic loss
- If P ≥ AVC, continue production (loss-minimising); if P < AVC, shutdown (loss-minimising)
8.4 Practical recap and relationships
- TR − TC maximum is the profit-maximising condition (MR = MC is another route to that same outcome).
- In the short run, firms may operate at a loss if they can cover variable costs and some fixed costs (i.e., TR ≥ TVC).
- In the long run, firms will adjust until they earn normal profit (PC-like behavior) or exit if profits are negative.
8.5 Mind map-style takeaway
- TR = P × Q
- AR = TR / Q
- MR = ΔTR / ΔQ
- Profit maximisation via TR − TC maximum or MR = MC
- Shutdown condition: produce if TR ≥ TVC; shutdown if TR < TVC
- Distinguish between economic profit, normal profit, and economic loss