Topics to be Discussed Chapter 7 n Measuring : Which Matter?

n Costs in the Short Run & Long Run

The Cost of n Long-Run Versus Short-Run Cost Curves Production n Production with Two Outputs--

Introduction Introduction n The production function measures the n To determine the optimal level of relationship between input and output. output and the input combinations, we must convert from the unit n Given the production technology, measurements of the production managers must choose how to produce. function to dollar measurements or (I.e., how many units ? ) costs.

Measuring Cost: Measuring Cost: Which Cost Matter? Which Cost Matter? n Accounting Cost n n Consider only explicit cost, the out of n Considers explicit and . pocket cost for such items as , n Opportunity cost is the cost associated with opportunities that are foregone by not putting resources in their salaries, materials, and property rentals highest valued use.

n n An expenditure that has been made and cannot be recovered--they should not influence a firm’s decisions. Cost in the Short Run Cost in the Short Run n Total output is a function of variable n (MC) is the cost of inputs and fixed inputs. expanding output by one unit. Since fixed cost have no impact on marginal n Therefore, the of production cost, it can be written as: equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the DVC DTC cost of the variable inputs), or MC = = DQ DQ TC = FC + VC

Cost in the Short Run Cost in the Short Run n Average Total Cost (ATC) is the cost per n The Determinants of Short-Run Cost unit of output, or average fixed cost n The relationship between the production (AFC) plus average variable cost (AVC). function and cost can be exemplified by This can be written: either increasing returns and cost or TFC TVC decreasing returns and cost. ATC = + Q Q TC ATC = AFC + AVC or Q

Cost in the Short Run Cost in the Short Run n The Determinants of Short-Run Cost n For Example: Assume the rate (w) n Increasing returns and cost is fixed relative to the number of n With increasing returns, output is increasing workers hired. Then: relative to input and variable cost and total cost DVC will fall relative to output. MC = n Decreasing returns and cost DQ n With decreasing returns, output is decreasing relative to input and variable cost and total cost will rise relative to output. VC = wL Cost in the Short Run Cost in the Short Run n Continuing: n Continuing: DVC = wDL DQ DMPL = DL wDL DL 1 MC = DL for a 1 unit DQ = = DQ DQ DMPL

Cost in the Short Run Cost in the Short Run n In conclusion: n Consequently (from the table): w n MC decreases initially with increasing MC = returns n 0 through 4 units of output MPL n MC increases with decreasing returns n …and a low marginal product (MP) n 5 through 11 units of output leads to a high marginal cost (MC) and vise versa.

Cost in the Short Run Cost in the Short Run n AVC and the Production Function n AVC and the Production Function VC AVC = Q Q APL = L VC = wL w AVC = wL AVC = AP L Q Cost in the Short Run Cost in the Short Run

n Observations n Summary n If a firm is experiencing increasing returns, n The production function (MP & AP) shows AP is increasing and AVC will decrease. the relationship between inputs and n If a firms is experiencing decreasing output. returns, AP is decreasing and AVC will n The cost measurements show the impact increase. of the production function in dollar terms.

Cost Curves for a Firm TC Cost Curves for a Firm 400 Price 100 MC ($ per VC ($ per year) unit) Marginal cost 300 75 decreases B initially then increases.

200 50 ATC A AVC 100 25 FC AFC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 Output (units per year) Output (units per year)

Cost Curves for a Firm Cost Curves for a Firm n The line drawn from n The ray drawn from the origin to the the origin to the TC TC tangent of the P tangent of the total P 400 400 variable : VC cost curve: VC n Its slope equals AVC n The slope of a 300 300 n The slope of a point B tangent equals the B on VC equals MC slope of the point. 200 n ATC at 8 units = MC 200 n Therefore, MC = AVC A A at 7 units of output n Output = 8 units . (point A) 100 100 F F C C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Output Output Cost Curves for a Firm Cost Curves for a Firm n Unit Costs n Unit Costs n AFC falls P n MC = AVC and ATC P continuously 100 MC at minimum AVC and 100 MC n When MC < AVC or ATC MC < ATC, AVC & 75 n Minimum AVC occurs 75 ATC decrease at a lower output 50 50 n When MC > AVC or ATC than minimum ATC ATC AVC AVC MC > ATC, AVC & due to FC 25 25 ATC increase AFC AFC 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 Output Output

Cost in the Long Run Cost in the Long Run

n Choosing Inputs n Choosing Inputs n Assumptions n A Decision Model

n Two Inputs: Labor (L) & capital (K) n C = wL + rK n Wage rate for labor (w) and rental rate for n Isocost: A line showing all combinations of L & capital (r) are determined in competitive K that can be purchased for the same cost markets

Cost in the Long Run Choosing Inputs

n Choosing Inputs n We will address how to minimize cost n Rewriting C as linear: for a given level of output.

nK = C/r - (w/r)L n We will do so by combining isocosts with DK = - w isoquants n Slope of the isocost: DL ( r)

n is the ratio of the wage rate to rental cost of capital. n This shows the rate at which capital can be substituted for labor with no change in cost. Producing a Given Producing a Given Output at Minimum Cost Output at Minimum Cost Capital Capital per per

year Isocost C2 shows quantity year Isocost C1 shows quantity K2 Q1 can be produced with Q1 can be produced with combination K2L2 or K3L3. combination K1L1.. However, both of these This is the low cost combination are higher cost combinations because it is tangent to Q1. than K1L1. A A K1 K1

Q1 Q1 K3

C0 C1 C2 C0 C1 C2

L2 L1 L3 L1 Labor per year Labor per year

Input Substitution When Input Substitution When an Input Price Change an Input Price Change Capital Capital This yields a new combination per per of K and L to produce Q1. year year Combination B is used in place If the price of labor of combination A. changes, the isocost curve The new combination represents becomes steeper due to the higher cost of labor relative the change in the slope -(w/L). B to capital and therefore capital K2 is substituted for labor. A A K1 K1

Q1 Q1

C1 C2 C1

L1 L2 L1 Labor per year Labor per year

Cost in the Long Run Cost in the Long Run

n Isoquants and Isocosts and the n The minimum cost combination can Production Function then be written as: - DK MPL MRTS = = MPL = MPK DL MPK w r

Slope of isocost line = DK = -w n Minimum cost for a given output will occur DL r when each dollar of input added to the production process will add an equivalent amount of output. Long-Run Versus Cost in the Long Run Short-Run Cost Curves

n Question: n Cost minimization with Varying Output Levels n If w = $10, r = $2, and MPL = MPK, which input would the producer use n A firm’s expansion path shows the more of? Why? minimum cost combinations of labor and capital at each level of output.

Long-Run Versus A Firm’s Expansion Path Short-Run Cost Curves Capital The expansion path illustrates per the least-cost combinations of n What happens to average costs when year labor and capital that can be used to produce each level of both inputs are variable (long run) output in the long -run. versus only having one input that is variable (short run)? Expansion Path

E D C B A

Labor per year

The Inflexibility of The Inflexibility of

CapitalShort-Run Production CapitalShort-Run Production per per E Begin with Q1 and Assume K is fixed year isocost AB which year (short-run) and output

yields K1L1. is increased to Q2. Combination K1L3 would have to be used on isocostEF. A

P K K 1 1 Q2

Q1 Q1

L1 B L1 B L3 F Labor per year Labor per year The Inflexibility of The Inflexibility of Short-Run Production Short-Run Production Capital E Capital E per If K is flexible (long -run), per The long -run expansion isocost line CD is used path is drawn as before.. year C year C yielding combination K2L2. CD is a lower cost level than EF. In the long -run, the firm A substitutes cheaper K A Expansion Path for L. K2 K2 K K 1 Q2 1 Q2

Q1 Q1

L1 L2 B D F L1 L2 B D F Labor per year Labor per year

Long-Run Versus Long-Run Versus Short-Run Cost Curves Short-Run Cost Curves

n Long-Run (LAC) n Long-Run Average Cost (LAC) n Constant n Increasing Returns to Scale n If input is doubled, output will double and n If input is doubled, output will more than average cost is constant at all levels of output. double and average cost decreases at all levels of output.

Long-Run Versus Long-Run Versus Short-Run Cost Curves Short-Run Cost Curves

n Long-Run Average Cost (LAC) n Long-Run Average Cost (LAC) n Decreasing Returns to Scale n In the long-run: n If input is doubled, the increase in output is n Firms experience increasing and decreasing less than twice as large and average cost returns to scale and therefor long-run average increases with output. cost is “U” shaped. Long-Run Versus Long-Run Average and Short-Run Cost Curves Marginal Cost Cost ($ per unit LMC n Long-Run Average Cost (LAC) of output n Long-run marginal cost leads long-run LAC average cost:

n If LMC < LAC, LAC will fall n If LMC > LAC, LAC will rise n Therefore, LMC = LAC at the minimum of LAC

Output

Long-Run Versus Long-Run Versus Short-Run Cost Curves Short-Run Cost Curves

n Question n Economies and Diseconomies of Scale n What is the relationship between long-run n average cost and long-run marginal cost n Increase in output is greater than the increase when long-run average cost is constant? in inputs. n Diseconomies of Scale n Increase in output is less than the increase in inputs.

Long-Run Versus Long-Run Versus Short-Run Cost Curves Short-Run Cost Curves

n Measuring Economies of Scale n Measuring Economies of Scale

Ec = Cost-Output Ec = (DC / C)/(DQ / Q) = %D in cost from a 1% increase in output Ec = (DC / DQ) /(C /Q) = MC/AC Long-Run Versus Long-Run Versus Short-Run Cost Curves Short-Run Cost Curves

n Therefore, the following is true: n The Relationship Between Short-Run n EC < 1: MC < AC and Long-Run Cost n Average cost indicate decreasing economies of scale n We will use short and long-run cost to n EC = 1: MC = AC determine the optimal plant size n Average cost indicate constant economies of scale

n EC > 1: MC > AC n Average cost indicate increasing diseconomies of scale

Long-Run Cost with Long-Run Cost with Constant Returns to Scale Constant Returns to Scale Cost Cost ($ per unit ($ per unit of output of output SAC1

Known: The SAC SMC1 for three plant sizes with constant returns to scale.

Output Output Q1

Long-Run Cost with Long-Run Cost with Constant Returns to Scale Constant Returns to Scale Cost Cost ($ per unit ($ per unit of output of output SAC1 SAC2 SAC1 SAC2 SAC3

SMC1 SMC2 SMC1 SMC2 SMC3

Output Output Q1 Q2 Q1 Q2 Q3 Long-Run Cost with Long-Run Cost with Constant Returns to Scale Constant Returns to Scale Cost With many plant sizes with SAC = $10 ($ per unit the LAC = LMC and is a straight line n of output Observation SAC1 SAC2 SAC3 n The optimal plant size will depend on the

anticipated output (e.g. Q1 choose SAC1,etc). SMC1 SMC2 SMC3 n The long-run average cost curve is the envelope LAC = of the firm’s short-run average cost curves. LMC

n Question n What would happen to average cost if an output level other than that shown is chosen?

Output Q1 Q2 Q3

Long-Run Cost with Economies and Long-Run Cost with Economies and Diseconomies of Scale Diseconomies of Scale Cost Cost SAC ($ per unit ($ per unit 1 SAC3 of output of output SAC2

Known: Three plant sizes with economies and diseconomies of scale.

SMC1 SMC3

SMC2

Output Output

Long-Run Cost with Economies and Long-Run Cost with Economies and Diseconomies of Scale Diseconomies of Scale Cost Cost SAC LAC SAC LAC ($ per unit 1 SAC3 ($ per unit 1 SAC3 of output of output SAC2 SAC2

SMC1 SMC1 SMC3 SMC3

SMC2 LMC SMC2

Output Output Long-Run Cost with Economies and Diseconomies Long-Run Versus of Scale Short-Run Cost Curves Cost SAC LAC ($ per unit 1 SAC3 of output n What is the firms’ long-run cost curve? SAC2 A n $10 Firms can change scale to change output in $8 the long-run. B n The long-run cost curve is the dark blue SMC If the output is Q a manager 1 SMC 1 portion of the SAC curve which represents 3 would chose the small plant SAC and SAC $8. LMC SMC 1 the minimum cost for any level of output. 2 Point B is on the LAC because it is a least cost plant for a given output.

Q1 Output

Long-Run Cost with Economies and Diseconomies Production with Two Outputs-- of Scale Economies of Scope

n Observations n Examples: n The LAC does not include the minimum n Chicken farm--poultry and eggs points of small and large size plants? Why n Automobile company--cars and trucks not? n University--Teaching and research n LMC is not the envelope of the short-run marginal cost. Why not?

Production with Two Outputs-- Production with Two Outputs-- Economies of Scope Economies of Scope

n Economies of scope exist when the joint n Advantages output of a single firm is greater than the output that could be achieved by two 1) Both use capital and labor. different firms each producing a single output. 2) The firms share management resources. n What are the advantages of joint production? n Consider an automobile company producing cars 3) Both use the same labor skills and and tractors type of machinery. Production with Two Outputs-- Economies of Scope Product Transformation Curve

Number O1 illustrates a low level of tractors of output. O2 illustrates n Production: a higher level of output with two times as much labor n Firms must choose how much of each to and capital. produce. O2 n The alternative quantities can be illustrated using product transformation curves. O1

Number of cars

Production with Two Outputs-- Production with Two Outputs-- Economies of Scope Economies of Scope n Observations n Observations n Product transformation curves are n There is no direct relationship between negatively sloped economies of scope and economies of n Constant returns exist in this example scale. n Since the production transformation curve n May experience economies of scope and is concave is joint production desirable? diseconomies of scale n May have economies of scale and not have economies of scope

Production with Two Outputs-- Production with Two Outputs-- Economies of Scope Economies of Scope n The degree of economies of scope measures n Interpretation: the in cost can be written: n If SC > 0 -- Economies of scope C(Q1) + C(Q 2) -C(Q1, Q 2) n SC = If SC < 0 -- Diseconomies of scope C(Q1, Q 2)

n C(Q1 ) is the cost of producing Q1

n C(Q2 ) is the cost of producing Q2

n C(Q1 Q2 ) is the joint cost of producing both products Example: Economies of Scope Example: Economies of Scope in the Trucking Industry in the Trucking Industry

n Issues n Questions: n Truckload versus less than truck load n Economies of Scale n Direct versus indirect routing n Are large-scale, direct hauls cheaper and more profitable than individual hauls by small trucks? n Length of haul n Are there cost advantages from operating both direct and indirect hauls?

Example: Economies of Scope Example: Economies of Scope in the Trucking Industry in the Trucking Industry

n Empirical Findings n Empirical Findings n An analysis of 105 trucking firms examined n Results four distinct outputs. n SC = 1.576 for reasonably large firm

n Short hauls with partial loads n SC = 0.104 for very large firms n Intermediate hauls with partial loads n Interpretation

n Long hauls with partial loads n Combining partial loads at an intermediate n Hauls with total loads location lowers cost management difficulties with very large firms.

Summary Summary

n Managers, investors, and n When there is a single variable input, as must take into account the opportunity in the short run, the presence of cost associated with the use of the determines the firm’s resources. shape of the cost curves.

n Firms are faced with both fixed and n In the long run, all inputs to the variable costs in the short-run. production process are variable. Summary Summary n The firm’s expansion path describes n A firm enjoys economies of scale when how its cost-minimizing input choices it can double its output at less than vary as the scale or output of its twice the cost. operation increases. n Economies of scope arise when the firm can produce any combination of the n The long-run average cost curve is the two outputs more cheaply than could envelope of the short-run average cost two independent firms that each curves. produced a single product.

Summary n A firm’s average cost of production can fall over time if the firm “learns” how to produce more effectively. n Cost functions relate the cost of production to the level of output of the firm.