Production and Cost Production Function Inputs Output (s) Cost Function At Given Output Level Inputs Unit Input Needed Price Based on Production Function Total Cost

Total Product Look at the slope Total Product Q Input (Labor) TP

Total Product Total Product Q Input (Labor) TP

Deriving the Average Product Curve Total Product Q Input (Labor) TP AP L L Q3Q3 Q2Q2 Q1Q1 P1P1 P2P2 P3P3

Total Product Q Input (Labor) TP MP L L Deriving the Marginal Product Curve

Critical Points in Average and Marginal Product Total Product Q Input (Labor) TP MP L L AP L A B C

Stages of Production Stage III MP L L AP L A B C Stage IStage II

Economic vs. Accounting Profit Economic profits from good (service) = Revenue from good (service) – Total Cost of making good (service) – Value of next best alternative Value of good (service) Value of next best alternative (aka “opportunity cost”) Accounting profits from good (services) = Revenue from good (services) – Total cost of making good (services)

Topics in Costs Estimating cost functions: Identifying Fixed from Variable Costs Short run costs Long run costs – scale economies Learning economies (“experience curves”) Economies of scope

Cost Functions In any tactical (short run) setting, some production drivers of a company are “fixed” while others are “variable” What is fixed and what is variable depends on the company, contracts drawn up, and the industry The Prestige Telephone Company case is (partially) an exercise in identifying fixed from variable costs. Also illustrates importance of accounting in economic decision making

Examples of Fixed and Variable Costs Fixed Cost Driver Variable Costs Driver Auto manufacturers  Physical Capital  Labor  Materials Universities  Tenured Faculty  Power (portion)  Non- tenured faculty  Staff

Cost Function Form of cost function depends on whether we are dealing with the short run or the long run Short run, some cost drivers are “fixed” (also to be shown in PTC example). Thus cost function is: C = Fixed Costs + Variable Costs Equation which relates total costs to output C = f(Q)

Estimating Cost Function Done by examining cost data (typically from income statements) and extrapolating cost function Some Fixed Costs are easily identified Some Variable Costs are also easily identified– the real issue is to determine the relationship between TVC and Q (linear or non-linear?) The trickiest items are “quasi-fixed-variable” costs: these have a fixed and variable component which must be separated

Quick notes about Costs C = Q What does F = 100 represent? What does AVC = 38 represent? What is cost of producing an additional chip, and what does it cover? Any insights into the production technology which may be gleaned from the cost function? What is Average Cost (AC)? Know what is C, F, TVC, AVC, AFC, and AC

Separating Fixed and Variable Costs Argued that some items have a fixed and variable component. How to identify each component? We must now make assumptions about the form of the cost function: linear, non- linear? “Constant” will be Fixed Cost Note how scatter plot suggests that a linear cost function seems appropriate

Cost Functions in general Can be either linear or non-linear If non-linear, MC depends on level of production Example: C = 20, Q + 0.5Q 2 MC = Q How to tell if your company has a linear or a non-linear cost function? ► Scatter plot of costs vs. output ► Run regressions ► Run a battery of test to test functional form

Total Cost Total Cost = Total Variable Cost + Total Fixed Cost TVC, TC Q TVC TC TFC

Deriving Average Fixed Cost TFC Q AFC Q

Deriving Average Variable Cost TVC Input (Labor) TVC AVC Q Minimum AVC AVC decreasing AVC increasing

Average Total Cost Q AFC ATC AVC AFC AVC ATC AFC AVC ATC

Deriving the Marginal Cost Curve TVC Q TC MC Q Minimum MC (Diminishing marginal returns to variable input) MC declining MC increasing

The Unit Cost Profile and Stages of Production Unit cost Q AFC AVC ATC MC Stage IStage IIStage III

Why does AC rise/fall? Short Run Reasons for AC rising/falling are very different depending on whether we are dealing with the short or the long run In the short run, at least one input is fixed Output rises from increase in variable inputs How variable inputs interact with the fixed input determines the shape of the Short run cost functions

Relation between Production and cost The production function implies the cost functions Diminishing marginal returns is the reason for increasing MC The profile of ATC, AVC, AFC and MC is very important for managerial decisions; learn to draw these curves accurately!

Quantity of labor Costs (dollars) Average product and marginal product Quantity of output MP MC Productivity & Cost Curve Relationship

Quantity of labor Costs (dollars) Average product and marginal product Quantity of output MP AP MC AVC Productivity & Cost Curve Relationship

Unit Costs Output For every plant capacity size... there is a short-run ATC curve there is a short-run ATC curve and every ATC has a minimum cost and every ATC has a minimum cost Long-run Production Costs

Unit Costs Output An infinite number of such cost curves can be constructed... Long-run Production Costs

The Long-run ATC just “envelopes” all of the short-run ATC curves Unit Costs Output Long-run Production Costs

Long-run ATC Unit Costs Output Long-run Production Costs

Unit Costs Output Long-run ATC Economies of scale Long-run ATC Curves

Unit Costs Output Long-run ATC Economies of scale Constant returns to scale Long-run ATC Curves

Unit Costs Output Long-run ATC Economies of scale Diseconomies Constant returns to scale Long-run ATC Curves

Unit Costs Output Where extensive economies of scale exist Long-run ATC Curves Long-run ATC

Unit Costs Output Where economies of scale are quickly exhausted Long-run ATC Curves Long-run ATC

A last word about... Minimum Efficient Scale - MES Decision on plant size should relate to the expected demand for the product Plant Size Expected Demand LRTC LRAC A $50000 $5.00 B C Although Plant C has lower cost per unit than plant A or B, you do not want to build the plant A or C if your estimated demand is units.