Finance 30210: Managerial Economics

Finance 30210: Managerial Economics Cost Analysis

Here’s the overall objective for the supply side Production Decisions Product Markets Factor Markets Factor Usage/Prices Determine Production Costs (We are here now) Demand determines markup over costs (Coming soon!) Supply/Demand Determines Factor prices (We have covered this)

Primary Managerial Objective: Minimize costs for a given production level (potentially subject to one or more constraints) Example: PG&E would like to meet the daily electricity demands of its 5.1 Million customers for the lowest possible cost Or Maximize production levels while operating within a given budget Example: Billy Beane and would like to maximize the production of the Oakland A’s while staying within payroll limits.

The starting point for this analysis is to think carefully about where your output comes from. That is, how would you describe your production process “is a function of” Production Level One or more inputs A production function is an attempt to describe what inputs are involved in your production process and how varying inputs affects production levels Note: We are not trying to perfectly match reality…we are only trying to approximate it!!!

Some production processes might be able to be described fairly easily: Sugar (Lbs) Your Time (Minutes) Water (Gallons) Lemons Paper Cups 8 Oz. Glasses of Lemonade With a fixed recipe for lemonade, this will probably be a very linear production process

Lemonade recipe (per 8oz glass) • Squeeze 1 Lemon into an 8 oz glass • Add 2 oz. of Sugar • Add 8 oz. of Water • Stir for 1 minute to mix 2 oz for each glass times 16 glasses = 2 lbs 1 Cup 1 glass available for sale 1 Lemon per glass 8 ounces per glass 1 minute per glass to stir each 8 oz glass

In fact, we could write the production function very compactly: • Lemonade recipe (per 8oz glass) • Squeeze 1 Lemon into an 8 oz glass • Add 2 oz. of Sugar • Add 8 oz. of Water • Stir for 1 minute to mix # of Lemonade “Kits” (one “kit” = 1 Lemon, 2oz. Sugar, 8 oz. Water, 1 Minute) Slope = 1

Inputs = Players Output = Wins Bill James used the following production function for wins… RS = Runs ScoredRA = Runs Given up

RS = Runs ScoredRA = Runs Given up

2011 Payroll Total: $201,698,030 Average (Per Player): $6,722, 968 Average (Per Win): $2,079,361 Average (Per Run): $232,639 2011 Payroll Total: $125,480,664 Average (Per Player): $5,228,361 Average (Per Win): $1,767,333 Average (Per Run): $191,866 RA = 657 RA = 756 .635 .428 RS = 654 RS = 867 Given their runs against, the Cub’s needed 1000 runs scored to match the Yankees win percentage!

To evaluate a player’s contribution to run production, numerous statistics are derived Runs Created On Base Percentage H = Hits W = Walks TB = Total Bases AB = At Bats H = Hits W = Walks HBP = Hit by Pitch AB = At Bats SF = Sacrifice Flies This was the “single number” in Moneyball

We can then start comparing productivity to cost… Derek Jeter ($15,729,365) Starlin Castro($567,000) 2011 2011 BA = .297 BA = .307

Some production processes might be more difficult to specify: How would you describe the production function for the business school? Input(s) Output(s)

How would you describe the production function for the business school? What is the “product” of Mendoza College of Business? YOU ARE! Finance Undergraduate (BA) Accounting 1 Year MBA (MBA) Marketing Management 2 Year MBA (MBA) Degrees South Bend EMBA (MBA) Chicago EMBA (MBA) Masters of Accountancy (MA) Masters of Nonprofit Administration (MA)

How would you describe the production function for the business school? How would you characterize the “inputs” into Mendoza College of Business • Facilities • Classroom Space • Office Space • Conference/Meeting Rooms • Personnel • Faculty (By Discipline) • Administrative • Administrative Support • Maintenance • Equipment • Information Technologies • Communications • Instructional Equipment Staff Labor Inputs Capital Inputs

How would you describe the production function for the business school? Have we left out an output? Notre Dame, like any other university, is involved in both the production of knowledge (research) as well as the distribution of knowledge (degree programs) Should the two outputs be treated as separate production processes?

The next question would be: What is your ultimate objective? Is Notre Dame trying to maximize the quantity and quality of research and teaching while operating within a budget? OR Is Notre Dame trying to minimize costs while maintaining enrollments, maintaining high research standards and a top quality education? Does it matter?

The Notre Dame Decision Tree Under the golden dome, resources are allocated across colleges to maximize the value of Notre Dame taking into account enrollment projections, research reputation, education quality, and endowment/resource constraints School of Architecture College of Arts & Letters College of Business School of Architecture School of Architecture Given the resources handed down to her, Dean Woo allocates resources across departments to maximize the value of a Business Degree and to maximize research output. Finance Department Management Department Marketing Department Accounting Department Graduate Programs Department chairs receive resources from Dean Woo and allocate those resources to maximize the output (research and teaching) of the department

Another issue has to do with planning horizon. Different resources are treated as unchangeable (fixed) over various time horizons It might take 5 years to design/build a new classroom building It could take 6 months to install a new computer network Now 6 mo 1 yr 2 yr 5 yr 10 yr It takes 1 year to hire a new faculty member Tenured faculty are essentially can’t be let go Shorter planning horizons will involve more factors that will be considered fixed

From here on, lets keep things as simple as possible… You produce a single output. There is no distinction as far as quality is concerned, so all we are concerned with is quantity. You require two types of input in your production process (capital and labor). Labor inputs can be adjusted instantaneously, but capital adjustments require at least 1 year “Is a function of” Total Production Capital (Fixed for any planning horizon under 1 year Labor (always adjustable)

Some definitions Marginal Product: marginal product measures the change in total production associated with a small change in one factor, holding all other factors fixed Average Product: average product measures the ratio of input to output Elasticity of Production: marginal product measures the change in total production associated with a small change in one factor, holding all other factors fixed

Over a short planning horizon, when many factors are considered fixed (in this case, capital), the key property of production is the marginal product of labor. For a given production function, the marginal product of labor measures how production responds to small changes in labor effort OR Diminishing Marginal Returns: As labor input increases, production increases, but at a decreasing rate Increasing Marginal Returns: As labor input increases, production increases, but at an increasing rate

Consider the following numerical example: We start with a production function defining the relationship between capital, labor, and production Capital is fixed in the short run. Let’s assume that K = 1 Suppose that L = 20.

Increasing Marginal Returns Quantity Decreasing Marginal Returns Negative Marginal Returns 96.8 Labor Maximum Production reached at L =70

Now, let’s calculate some of the descriptive statistics Recall, K = 1

The properties of the marginal product of labor will determine the properties of the other descriptive statistics MP hits a maximum at L = 35 1 Elasticity of production less than one indicates MP<AP (Average product is falling) Elasticity of production greater than one indicates MP>AP (Average product is rising)

Cost Minimization: Short Run Capital costs are fixed in the short run! The cost function for the firm can be written as Given the costs of the firm’s inputs, the problem facing the firm is to find the lowest cost method of producing a fixed amount of output

Cost Minimization: Short Run is fixed Remember…this needs to be positive!! First Order Necessary Conditions

Marginal costs refer to changes in total costs when production increases With capital fixed, marginal costs are only influenced by labor decisions in the short run Average (Unit) costs refer to total costs divided by total production Average fixed costs fall as output increases

Cost Minimization: Short Run is fixed Recall that lambda measures the marginal impact of the constraint. In this case, lambda represents the marginal cost of producing more output Marginal costs are increasing Marginal costs are decreasing

Marginal Cost vs. Average Cost Costs AC Minimum AC occurs where AC=MC MC When AC is less than MC, AC rises When AC is greater than MC, AC Falls

Marginal Cost vs. Average Cost Costs AC MC If production exhibits increasing marginal productivity, then Average Costs decline with production (it pays to be big!)

Back to our example: Minimize costs for a given production level (potentially subject to on or more constraints) Let’s imagine a simple environment where you can take the cost of labor as a constant. Suppose that labor costs $10/hr and that you have one unit of capital with overhead expenses of $30. You have a production target of 450 units: =1 Objective Constraint

With only one variable factor, there is no optimization. The production constraint determines the level of the variable factor. 450 Quantity Labor 450 Units of production requires 60 hours of labor (assuming that K=1)

Let’s imagine a simple environment where you can take the cost of labor as a constant. Suppose that labor costs $10/hr and that you have one unit of capital with overhead expenses of $30. You have a production target of 450 units: =1 Total Costs Objective Constraint Solution: L = 60 Suppose that you increase your production target to 451. How would your costs be affected? Total Costs = 30 + 10(60) = $630 Average Costs = $630/450 = $1.40 Average Variable Costs = $600/450 = $1.33

If the marginal product of labor measures output per unit labor, then the inverse measures labor required per unit output We also know that the average variable cost is related to the inverse of average product

Properties of production translate directly to properties of cost MC<AVC. Average Variable Cost is falling MC>AVC. Average Variable Cost is Rising MC hits a minimum at L = 35 Labor Elasticity of production less than one indicates MP<AP (Average product is falling) Elasticity of production greater than one indicates MP>AP (Average product is rising)

For now, we are only dealing with the cost side, but eventually, we will be maximizing profits. =1 Total Costs Objective Constraint We just minimized costs of one particular production target. Maximizing profits involves varying the production target (knowing that you will minimize the costs of any particular target). There should be one unique production target that is associated with maximum profits: Maximum Profits Optimal Factor Use

Recall the alternative management objective: Maximize production levels while operating within a given budget Let’s imagine a simple environment where you can take the cost of labor as a constant. Suppose that labor costs $10/hr and that you have one unit of capital with overhead expenses of $30. You have a production budget of $630: Total Output Available budget Constraint Objective

Just like before, there is no optimization. The budget constraint determines the level of the variable factor. 630 Cost Labor $630 budget restricts you to 60 hours of labor (assuming that overhead = $30)

Total Output Available budget Constraint Objective Now, if we were to think about altering the objective we would be considering the effect on production of a $1 increase in the budget: Change in production Now, take the profit maximizing condition and flip it Change in Budget Both managerial objectives yield the identical result!!! Optimal Factor Use

In the long run, we can adjust both inputs. Therefore, we need to look at how production changes as both factors adjust. Labor L = 33 L = 13 Capital K = 2 K = 30 An isoquantrefers to the various combinations of inputs that generate the same level of production

In the long run, we need to think about the relative productivity of each factor. Labor Capital The Technical rate of substitution (TRS) measures the amount of one input required to replace each unit of an alternative input and maintain constant production

Recall some earlier definitions: Marginal Product of Labor Marginal Product of Capital Labor If you are using a lot of capital and very little labor, TRS is small Capital

A key property of production in the long run has to do with the substitutability between multiple inputs. The elasticity of substitutionmeasures curvature of the production function (flexibility of production)

Technical rate of Substitution measures the degree in which you can alter the mix of inputs in production. Consider a couple extreme cases: Perfect substitutes can always be can always be traded off in a constant ratio Perfect compliments have no substitutability and must me used in fixed ratios Labor Labor Elasticity is Infinite Elasticity is 0 Capital Capital

Cost Minimization: Long Run is variable

Cost Minimization: Long Run First Order Necessary Conditions

Again, back to our example Let’s imagine a simple environment where you can take the cost of labor and the cost of capital as a constant. Suppose that labor costs $10/hr and that capital costs $30 per unit. You have a production target of 450 units: Total Costs Objective Constraint Now we have two variables to solve for instead of just one!

Consider two potential choices for Capital and Labor L = 13 K = 30 TC = 30*30 + 13*10 = $1030 AC = $1030/450 = $2.29 L = 33 K = 2 TC = 30*2 + 33*10 = $390 AC = $390/450 = $0.86 This procedure is relatively labor intensive This procedure is relatively capital intensive With more than one input, there should be multiple combinations of inputs that will produce the same level of output

Finance 30210: Managerial Economics