**Managerial Economicsin a Global Economy** Chapter 7 Cost Theory and Estimation

**The Nature of Costs** • Explicit Costs • Accounting Costs: actual expenditures on resources • Economic Costs • Implicit Costs: returns on inputs owned by the firm • Opportunity Costs (Economic Costs): costs of all the inputs, whether owned by the firm or not. • Example 1. • Suppose that a firm purchased raw materials by 100, kept in the inventory. • If the price fell to 60. • Accountant cost = 100 • Economic Cost (relevant) = 60 • We can’t sell by more than 60.

**Example 2.** • A machine purchased for 1000. If we use a linear depreciation for 10 years. • After 10 years, the accounting value = zero. • Suppose that after 10 years, the firm can sell the machine for 120. • The economic cost of the machine at year 11 = 120. • We can sell it at that value. • Relevant Costs • Incremental Costs: the change in total costs from implementing a particular managerial decision, e.g., introducing a new product line, undertaking a new advertising campaign, or the production of a previously purchased component. • Sunk Costs are Irrelevant: the costs that are not affected by the decision, they are irrelevant or Sunk Costs.

**Short-Run Cost Functions** • Total Cost = TC = f(Q) • Total Fixed Cost = TFC • Total Variable Cost = TVC • TC = TFC + TVC • Average Total Cost = ATC = TC/Q • Average Fixed Cost = AFC = TFC/Q • Average Variable Cost = AVC = TVC/Q • ATC = AFC + AVC • Marginal Cost = TC/Q = TVC/Q

**Short-Run Cost Functions**

**Average Variable Cost** • AVC = TVC/Q = w/APL • Note that AVC = TVC/Q = wL/Q • But APL = Q/L and 1/APL = L/Q • By substitution • AVC = w . 1/APL = w/APL • Marginal Cost • TC/Q = TVC/Q = w/MPL • Note that • MC = TVC/ Q = w (L) / Q • But • MPL = Q / L and 1/MPL = L / Q • Since w is constant and by substitution; • MC = W . 1/MPL = w/MPL

**Long-Run Total Cost = LTC = f(Q)** • Long-Run Average Cost = LAC = LTC/Q • Long-Run Marginal Cost = LMC = LTC/Q

**Derivation of Long-Run Cost Curves**

**Relationship Between Long-Run and Short-Run Average Cost** Curves

**Possible Shapes of the LAC Curve**

**Plant Size and Economies of Scale** • Reasons of economies of scale: • Specialization • Technological reasons (diameter of pipes) • Financial Reasons • Quantity discounts • Interest discounts • Advertising discounts Theoretical LAC Economies of Scale Diseconomies of Scale

**Economies of Scope** • Lowering costs when a firm produces tow or more products together than producing each one alone • S = {C(Q1) + C(Q2) – C(Q1+Q2)} / C(Q1+Q2) • (scope) • e.g., • If Q1+Q2 = 15 • If C(Q1) = 12 and C(Q2) = 6 then; • S = ((12+6)) – 15 / 15 = .2 • There is a 20% saving in costs the bigger the economies of scope

**Learning Curve** • Shows the decline in the average input cost of production with rising cumulative total outputs over time. • Average Cost of Unit Q = C = aQb • C = average input cost • a = average cost of the first unit of output • b = negative • Note: • If b is high, the faster is the decline in input cost • If b is small the smaller is the decline in input cost

**The Learning Curve**

**Estimation Form: ** • log C = log a + b Log Q • e.g., if estimated regression is: • Log C = 3 – 0.3 log Q At Q = 100 • Log C = 3 – 0.3 log(100) = 3 – 0.3(4.605) = 3 – 1.382 = 1.616 At Q = 200 Log C = 3- 0.3 log(200) = 3 – 0.3(5.2989) = 3 – 1.589 = 1.411 Average costs is going down as output is increasing over time.

**Cost-Volume-Profit Analysis (Break Even)** • Note: • Total Revenue = TR = (P)(Q) • Total Cost = TC = TFC + (AVC)(Q) • Breakeven Volume TR = TC • Or: • (P)(Q) = TFC + (AVC)(Q) • QBE = TFC/(P - AVC) • Target output • QT = (TFC + ΠT) / (P – AVC)

**Cost-Volume-Profit Analysis** P = 40 TFC = 200 AVC = 5 QBE = 40

**e.g., Break even output** • If TFC = 200 P = 10 AVC = 5 • QBE= (200/(10-5) = 40 • Since P = 10 • TR = 10(40) = 400 • TC = TFC + P(AVC) = 200 + 40(5) = 400 e.g., target output • If the firm wants to earn 100 as a target profit what is the target output • QT = (200 + 100) / (10-5) = 60 • Note that • TR = 10(60) = 600 • TC = 200 + 5(60) = 500 • Π = TR – TC = 600 – 500 =100 • Which is the target profit

**Operating Leverage** • Operating Leverage = TFC/TVC Degree of Operating Leverage = DOL

**TC’ has a higher DOL than TC and therefore a higher QBE**

**Empirical Estimation Data Collection Issues** • Opportunity Costs Must be Extracted from Accounting Cost Data • Costs Must be Apportioned Among Products • Costs Must be Matched to Output Over Time • Costs Must be Corrected for Inflation

**Empirical Estimation** Functional Form for Short-Run Cost Functions Theoretical Form Linear Approximation

**Theoretical Form** Linear Approximation

**Empirical Estimation long-Run Cost Curves** • Cross-Sectional Regression Analysis • Engineering Method • Survival Technique Actual LAC versus empirically estimated LAC’