FIN 30210: Managerial Economics

FIN 30210: Managerial Economics Cost Analysis

Here’s the overall objective for the firm Product Markets Production Decisions Factor Markets Demand and market structure determine the markup of price over cost Businesses take factor prices as given Factor Usage/Prices Determine Production Costs Coming Soon You are here

Example: Moneyball - The Art of Winning an Unfair Game Michael Lewis

What is Billy Beane’s Problem…No Money! Final Standings W/L: 103/58 WP: .640 Dollars/Win: $1.36M Final Standings W/L: 103/59 WP: .636 Dollars/Win: $388K As a small market team, the A’s were pretty near the bottom in terms of payrolls, but they made every dollar count! 2002 Major League Payrolls

What is Billy Beane’s Objective? Minimize costs for a given production level (potentially subject to one or more constraints) Billy Beane is looking for the cheapest way for the Oakland A’s to win the world series OR Maximize production levels while operating within a given budget Billy Beane and would like to maximize the production of the Oakland A’s while staying within payroll limits.

Enter Paul DePodesta (a.k.a. Peter Brand) Can we define a Production Function for a Baseball Club? Billy Beane Paul DePodesta Inputs = Players Output = Wins Winning Percentage RS = Runs ScoredRA = Runs Given up Brad Pitt as Billy Beane Jonah Hill as “Peter Brand” Bill James

For a team with the league average runs against, here’s what this looks like Winning Percentage In 2015, the league average was 688 Runs Scored

For a fixed number of runs against, hitting homers does have diminishing returns! League Range Winning Percentage In 2015, the league average was 688 Winning Percentage Change Change Runs Scored

For a fixed number of runs for, runs against also has diminishing returns! League Range In 2015, the league average was 688 Change Winning Percentage Runs Against

Let’s look at the Cubs vs. The Yankees Predicted Winning Percentage Chicago Cubs (2015) Total Payroll: $120,337,385 Avg. Salary: $3,760,543 Wins/Losses: 97/65 WP: .598 RS: 689 RA: 608 Dollars/Win: $1,240,591 League Range .562 For the Yankees to match the Cubs win percentage, they would need 800 runs New York Yankees (2015) Total Payroll: $217,758,751 Avg. Salary: $7,258,619 Wins/Losses: 87/75 WP: .537 RS: 764 RA: 698 Dollars/Win: $2,502,974 .545 Runs Scored

To evaluate a player’s contribution to run production, numerous statistics are derived On Base Percentage Runs Created H = Hits W = Walks HBP = Hit by Pitch AB = At Bats SF = Sacrifice Flies H = Hits W = Walks TB = Total Bases AB = At Bats Peter Brand: “It's about getting things down to one number. Using the stats the way we read them, we'll find value in players that no one else can see”

So, let’s evaluate a couple possible players to help the Yankees catch up to the Cubs Runs Created H = Hits W = Walks TB = Total Bases AB = At Bats Bryce Harper (Washington Nationals) 2015 Salary: $5,000,000 Albert Pujols (L.A. Angels) 2015 Salary: $25,000,000 On Base Percentage H = 172 W = 124 HBP = 5 AB = 521 SF = 4 H = 172 W = 124 TB = 338 AB = 521 H = 147 W = 50 HBP = 6 AB = 602 SF = 3 H = 147 W = 50 TB = 289 AB = 602 H = Hits W = Walks HBP = Hit by Pitch AB = At Bats SF = Sacrifice Flies

New York Yankees Total Payroll: $217,758,751 +$ 5,000,000 $222,758,751 RS: 764 + 155 = 919 RA: 698 WP: .634 Winning Percentage With Bryce Harper League Range .562 .545 New York Yankees (2015) Total Payroll: $217,758,751 +$ 25,000,000 $242,758,751 RS: 764 + 87 = 851 RA: 698 WP: .597 With Albert Pujols Runs Scored

Can we apply “Moneyball” more generally? 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: Notre Dame wants to maximize it’s educational/research output given its budgetary limitations

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)

We have several performance metrics for inputs 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. Increasing Marginal Returns: As labor input increases, production increasesat an increasing rate Diminishing Marginal Returns: As labor input increases, production increases, but at a decreasing rate

Note that the behavior of marginal product influences average product. Diminishing Marginal Returns: As labor input increases, the marginal product decreases and pulls the average down Increasing Marginal Returns: As labor input increases, marginal product increases and pulls the average up

Often, a production process will display both characteristics. Increasing Marginal Returns: As labor input increases, marginal product increases and pulls the average up Diminishing Marginal Returns: As labor input increases, the marginal product decreases and pulls the average down Increasing Marginal Returns: As labor input increases, marginal product increases and pulls the average up Diminishing Marginal Returns: As labor input increases, the marginal product decreases and pulls the average down

Example: Baseball Winning Percentage Winning Percentage In 2015, the league average was 688 Winning Percentage Change Change Runs Scored Increasing Marginal Returns: As labor input increases, marginal product increases Diminishing Marginal Returns: As labor input increases, the marginal product decreases

Suppose we minimize total costs for a fixed capital stock This is a fixed cost in the short run NOTE: With the capital stock, this is a rather trivial problem. There is only one choice for labor that gets the job done. Bear with me…there is a reason for doing this! So, minimizing the total costs associated with producing a set quantity of output would look like this

Suppose we minimize total costs for a fixed capital stock First, write down the lagrangian…. NOTE: With the capital stock fixed, this is a rather trivial problem. There is only one choice for labor that gets the job done. Bear with me…there is a reason for doing this! We have one minimization condition and a constraint Recall that the multiplier measures the marginal impact of the constraint. In this case, it would be the impact on costs of altering the production level…marginal cost!

Now, imagine varying the quantity constraint Remember, lambda gives you marginal cost Every choice for quantity will have a choice for labor associated with it. Maximum Efficiency!! (Minimum Marginal Cost)

Alternatively, we could maximize production given a fixed budget Again, write down the lagrangian…. NOTE: With the capital stock fixed, this is a rather trivial problem. There is only one choice for labor that gets the job done. Bear with me…there is a reason for doing this! Again, we have one minimization condition and a constraint Recall that the multiplier measures the marginal impact of the constraint. In this case, it would be the impact on production of altering the budget!

Now, imagine varying the cost constraint Remember, lambda gives you output per dollar Every value for the cost constraint implies an affordable choice for labor Maximum Efficiency!! (Maximum Output per dollar spent)

Duality: The two approaches coincide at the optimal choice Over or Underutilization of labor results in a marginal product that is below the optimum (marginal costs are above minimum) Maximum Efficiency!!

Important: The profit maximizing need not (and generally will not) coincide with the maximum efficiency choice! Minimum Marginal Cost!! Typical Profit Maximizing!! Maximum Efficiency!!

Properties of production translate into properties of cost Marginal Cost Average Cost Average Cost Marginal Cost Minimum Average Cost

Suppose that wages go up by 10% Maximum Efficiency!!

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.

Consider the following numerical example:

Increasing Marginal Returns Decreasing Marginal Returns Negative Marginal Returns Decreasing Getting Flatter Getting Steeper

Average Product is Increasing Average Product is Decreasing L = 53

Suppose we take on the first managerial objective. Let’s minimize the production costs associated with producing 450 units. First, write down the lagrangian…. We have one minimization condition and a constraint L = 60

Quantity Labor (Approximately)

Average Product is Increasing Average Product is Decreasing 60 L = 53 Q=410 L = 35 Q=243

Minimum Average Cost L = 53 Q= 410 MC = $1.35 AC = $1.36 L = 35 Q=243 MC= $0.96 AC = $1.56 60 Minimum Marginal Cost

Suppose that the wage rate rose to $15 (A 50% increase) NOTE: With the capital stock fixed at 1, this is a rather trivial problem. There is only one choice for labor that gets the job done. Bear with me…there is a reason for doing this! First, write down the lagrangian…. We have one minimization condition and a constraint

Suppose the wage rate rose to $15 (A 50% increase) $3.20 50% $2.13 60

Side note: Labor demand is perfectly inelastic in the short run Wage Rate w = $15 w = $10 Labor 60

In the long run, we have an additional metric to gauge factor performance Labor Recall some earlier definitions: Marginal Product of Labor Marginal Product of Capital 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

We also need a measure of the flexibility of production The elasticity of substitutionmeasures curvature of the production function (flexibility of production)

Perfect compliments have no substitutability and must me used in fixed ratios Perfect substitutes can always be can always be traded off in a constant ratio

Now we minimize total costs for a variable capital stock First, write down the lagrangian…. We have two minimization conditions and a constraint Set the lambdas equal to each other Solve for lambda

At the optimal choice for capital and labor, the technical rate of substitution is equal to the relative price of the two factors Labor Capital

Again, back to the numerical example Labor L = 33.5 L = 15.5 Capital K = 1.98 K = 7.35 An isoquantrefers to the various combinations of inputs that generate the same level of production

Consider two potential choices for Capital and Labor Labor L = 33.5 K = 1.98 TC = 30(1.98) + 10(33.5)= $394.40 AC = $394.40/450 = $0.87 This procedure is relatively labor intensive 33.5 L =15.5 K = 7.35 TC = 30(7.35) + 10(15.5) = $375.50 AC = $375.50/450 = $.83 This procedure is relatively capital intensive 15.5 Capital 7.35 1.98

Consider two potential choices for Capital and Labor L = 33.5 K = 1.98 TC = 30(1.98) + 10(33.5)= $394.40 AC = $394.40/450 = $0.87 Labor 33.5 L=33.5 and K=1.98 can’t be optimal because we could produce the same quantity for $0.49 – $0.13 = $0.36 less. Lowering production by 1 unit (keeping capital fixed and lowering labor) will lower total costs by (approximately) $0.49 Capital 1.98 Raising production by 1 unit (keeping labor fixed and raising capital) will increase total costs by (approximately) $0.13

Consider two potential choices for Capital and Labor L =15.5 K = 7.35 TC = 30(7.35) + 10(15.5) = $375.50 AC = $375.50/450 = $.83 Labor L=15.5 and K=7.35 cant be optimal because we could produce the same quantity for $0.49 –$0.19= $0.30 less. Raising production by 1 unit (keeping capital fixed and increasing labor) will raise total costs by (approximately) $0.19 15.5 Capital 7.35 Lowering production by 1 unit (keeping labor fixed and lowering capital) will lower total costs by (approximately) $0.49

The minimization looks like this First, write down the lagrangian…. We have two minimization conditions and a constraint

FIN 30210: Managerial Economics