Executive Summary Midterm Exam MECN 430 Winter 2016
Cost Concepts I. Key Terms Used in Class • •
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Variable costs: costs that change as the firm varies its output. Fixed costs: costs that remain the same as the firm varies its output, even when it produces an output of zero. Marginal cost: the change in total cost that result from increasing output by one unit. Equivalently: the cost of the last unit produced. Average (total) cost: the cost per unit on average, across all units produced. Sunk costs: costs that have already been incurred as a result of past decisions. Other terms: o Total cost: the sum of the firm’s ongoing variable and fixed costs plus capital charge on the firm’s assets and salvage value. o Full-Reinvestment Full-Reinvestment total cost: the firm’s “all-in” costs plus the capital charge for the firm’s assets. o Average total cost (ATC) or Full-Reinvestment average total cost (FR-ATC): same as above, divided by the number of units produced.
II. Example Firm has … 1. Variable costs of $15 per ton up to full capacity output of 1,000,000 tons per year 2. Fixed cost of $2,000,000 per year 3. Incurred a one-time entry cost of $50,000,000 to come into this market. Annual cost of capital is 10 percent. 4. For simplicity, we assume firm’s assets have no salvage value. Totals • Total Variable Cost (denoted by TVC ) = 15 Q Total Fixed Cost (denoted by TFC ) = $2,000,000 per year • Total Cost (denoted by TC ) = 15Q + 2,000,000 • Annualized capital charge: 0.10*$50,000,000 = $5,000,000 per year • • Full-reinvestment total cost (denoted by FR-TC ) = 15Q + 7,000,000 Notice the “build-up” relationship here: TC = • = TVC + + TFC • FRTC = = TC + + annual capital charge
Question: Why do
we use a “capital charge”? Answer: a capital charge, in effect, converts “onetime” entry or investment costs into an annualized cost flow. It allows an “apples-to-apple “ apples-to-apples” s” comparison of all of of the costs of doing business (those incurred incurred on a year-in, year-out basis, as well as one-time costs) that the firm would have to cover (See “Notes on the Microeconomics of Cost” for more information). information). The capital charge is an opportunity cost of the firm’s investment in the business (i.e. the $1 billion to build a smelter). If you can’t cover the rate of return on that initial investment, it implies your next best investment opportunity opportunity at the time would have had ultimately a better pay-off. As a result, a firm only makes economic profits if they can cover the cost of running the business ( ATC ) plus the rate of return on investments (capital charge) = FR-ATC . Averages AVC = • = Total variable cost/quantity cost/quantity = TVC /Q = 15 • = Total cost/quantity = TC /Q = 15 + 2,000,000/ Q ATC = FR-ATC = • = Full-reinvestment cost/quantity = FR-TC /Q = 15 + 7,000,000/ Q Marginal cost MC is • is the cost of an additional unit produced. TC = = 15Q + 2,000,000; if Q increases by 1, TC is the slope of TC . increases by 15. For linear cost functions, MC = AVC is
III. Salvage Value or Direct One-Time Cost of Exit • •
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What if, upon exit, we could receive a one-time salvage value for our assets of $30,000,000? Then, in defining total cost and average total cost we would want to include this as an opportunity cost of staying in business. Again, to achieve an “apples-to-apples” comparison, we want to convert the one-time salvage value into an annualized cost flow, since the need to cover the salvage value is an opportunity cost of staying in business. Using our discount rate of 10 percent, we have an annualized salvage value of $3,00,000 per year. We included this annualized value in defining total cost. Thus, with a salvage value: TC = = TVC + + TFC + + annualized salvage (or redeployment) value.
IV. Relevant Costs: What Decisions Do We Use These Concepts For? •
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Output optimization: In choosing how much output to produce, a price-taking firm maximizes profit by comparing price to marginal cost, i.e., it produces if P MC . Long-run withdrawal of capacity (exit price): As a condition of keeping its capacity in the industry, as opposed to permanently closing it down and exiting from the industry, the firm must expect to cover the minimum level of its average total cost, i.e., P min ATC . For linear cost functions, this minimum is achieved at capacity. Entry or reinvestment: As a condition of entering the industry in the first-place, or reinvesting in worn-out assets, the firm must expect to cover the minimum level of its fullreinvestment average total cost, i.e., P min FR-ATC . For linear cost functions, this minimum is achieved at capacity.
Demand Concepts Elasticities •
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Price elasticity of demand (often denoted ε ): ): Percentage change in quantity demanded per one percent change in price. o ε = = (dQ/dP)*(P/Q) o Elasticity ≠ slope! If demand curve is linear, X = = a – bP, the coefficient b is not the price elasticity of demand Other elasticities. Suppose quantity demanded depends on some other demand driver whose level Z could is Z ( ( Z could be income, prices of a substitute good, advertising, and so on). The “ Z ” elasticity of Z /Q). For example, an increase in demand (e.g., income elasticity of demand) is given by ( dQ/dZ )( )( Z income (e.g., GDP) can lead the demand function to shift out (i.e., for each price, the quantity demanded at that price increases). The income elasticity of demand is positive in that case; it tells you (roughly) how big the shift is. The cross-price elasticity of demand indicates the relationship between two goods. A positive cross-price elasticity indicates that the two goods are substitutes, while a negative cross-price elasticity indicates that they are complements.
Competitive Markets I. The “Runs” • Short run: period of time in which price dynamics determined by output adjustments of active or near-active firms. • Long run: period of time in which price dynamics determined by output adjustments of active or near-active firms as well as entry of new capacity and withdrawal and attrition of existing capacity. II. Short-Run Equilibrium •
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A short-run equilibrium is defined by the condition: Market price is such that Quantity Supplied = Quantity Demanded, i.e., S(P) = D(P). Provided that market demand and firms’ costs do not change, this is a stable situation in the short run in that there are no forces at work for price to change. Short-run supply curve can be constructed from data on variable costs. Constructing short-run short-run supply curve from cost data with constant MC : Take the MC of of incumbent firms, arrange in “merit order” from lowest to highest, and draw a curve which has jumps at prices prices equal to the marginal marginal cost of the firm, firm, where the size of the jump equals the total capacity of the firm with this marginal cost.
III Long-Run Supply Curves and Prediction of Long-Run Trends •
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The long-run market supply curve tells us the how much output would be forthcoming at various possible market prices in the long run. Constructing long-run supply curve from cost data: Take the min- ATC of of incumbent firms (calculated at full capacity operation, i.e., the “exit price”), arrange in “merit order” from lowest
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to highest and append the min-FR-ATC of of a typical entrant (calculated at full capacity operation, i.e., the “entry price”). The long-run equilibrium price is the price at which there is no entry or exit. If demand is expanding over the long run or equipment wears out, we will end up at price equal ATC of to FR- ATC of the typical entrant (assuming nothing else changes). If equipment does not wear out, that is, all production capacity has infinite lifetime, and if all firms have comparable cost structures, then prices between min- ATC and and min-FR-ATC are are potentially sustainable. This is because there is no exit and no entry in that range. In practice, the assumption that equipment does not wear out rarely applies.
Basic Monopoly Pricing •
Marginal revenue: the gain or loss in total revenue from selling one more unit of output. o Formally: the derivative of total revenue with respect to Q o Example: Demand curve is given by Q = 80 – 4 P. Invert this to get: P = 20 – ¼ Q. This is the inverse demand curve. Total revenue is TR = P*Q = 20Q – ¼ Q2. MR = dTR/dQ = 20 – ½Q. o In general, if P=a – bQ, then it follows that MR = dTR/dQ = a – 2bQ. Thus for for linear demand curves, the MR curve has the same intercept as the inverse demand curve on the P-axis and twice the slope. o The margin rule states that ( P-MC )/ )/P=-1/ε at at the profit-maximizing point (here ε is is the price elasticity of demand). o
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You can solve the Margin Rule for the price to obtain
, where here we’re �−1 =
treating ε as a positive number. This equation will yield the optimal price if the demand curve is isoelastic – that is, if the demand curve has the same elasticity at every point. If the demand curve is not isoelastic, then it almost certainly increases in elasticity as the price increases. In these cases, the true optimal price will be between the current price and the result of applying the margin rule. You don’t know exactly where unless you know a lot about the curvature of the demand curve. Note the difference with perfect competition: in perfectly competitive markets, firms are price-takers and therefore MR=P.
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Monopolist’s profit-maximizing profit-maximizing quantity and price: Profit-maximizing quantity is found by equating MR to MC . The profit-maximizing price is found by plugging optimal quantity into the inverse demand curve. o Example: Same as above, but suppose MC = = 10. MR = MC implies implies 20 – ½ Q = 10, or Q = 20. o Optimal price is 20 – ¼ (20) = 15.
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What about covering FR-ATC ? To maximize total profit, you do not set a price to explicitly FR ATC . (e.g., you do not set price to equal FR- ATC ATC or “cover” FR ATC or to achieve a certain mark-up over FR-ATC ). ). o You set prices to maximize profit based on the conditions of demand (marginal revenue) and the costs whose level is affected the pricing decision (marginal cost). o If the firm has made “wise” market entry and investment decisions, then setting price ATC . and output on the basis of the MR = MC condition condition should allow it to cover its FR- ATC
And even if it cannot cover its FR-ATC (e.g., (e.g., because its market entry and investment decisions turned out to be unwise or unlucky), pricing based on MR = MC will will at least minimize losses. •
Relevant costs for a monopolist : More generally, the costs that are relevant for decision making by a monopolist depend on what that decision is: o Output-pricing decisions: If the monopolist is making an output/pricing decision, the costs that are relevant to that decision are those depend on the level of output the firm produces. This is marginal cost . o Dropping a product line/withdrawing from a line of business : If the monopolist is making a decision to drop a particular product line or withdrawing from a particular line of business, the costs that are relevant are those that are avoidable (i.e., “go away”) if the firm withdraws from the business of producing and selling the product. That is the exit decision is driven by total non-sunk costs. This is the same decision criteria developed for competitive firms.
