Managerial EconomicsTheory and Estimation of Costs

Aalto UniversitySchool of Science

Department of Industrial Engineering and Management

January 12 – 28, 2016Dr. Arto Kovanen, Ph.D.

Visiting Lecturer

There are alternative types of costs Opportunity cost is the value of forgone opportunity

(could be indirect and implicit) Out-of-pocket cost (direct and explicit) Incremental cost varies the range of options available Sunk cost does not vary by the scale of production

Firm’s cost structure reflects its production process, driven by production technology and input prices

Usually firms are “price takers” in the market for inputs

Total variable costs (TVCs) are associated with the variable inputs, such as labor, materials, and so on

Production costs

Total fixed costs (TFCs) are associated with the use of fixed inputs (some may be variable in the long run)

Total costs (TCs) represent the total of TVC and TFC

Marginal cost (MC) is the change in total cost associated with a change in output

MC = dTC/dQ = dTVC/dQ + dTFC/dQ Relationship between marginal product and

marginal cost: when MP is falling, MC is increasing (due to the diminishing returns)

Production costs (cont.)

Formally, this can be expressed as follows:MC = dTVC/dQ = w*dL/dQ = w*(1/MP) where MP is the marginal product of labor input Short-run cost function tells what is the

minimum cost necessary to produce a particular level of output

Average total cost (AC) is the average cost per unit of all inputs

Average variable cost (AVC) is the per-unit cost of using variable inputs

Average fixed cost (AFC) is the per-unit cost of fixed inputs

Production costs (cont.)

Production costs (example)

Plot, TC, TVC, AC, AVC and MC curves Discuss the relationship between MC and AVC What can we say about AFC from the graph? How does a change in the cost of fixed input

affect the position of AC curve? Discuss! How does a change in the unit cost of variable

input affect the position of MC, AC, and AVC curves? Discuss!

Example: unit cost of labor declines.

Production costs (example)

In the long-run, (almost) all inputs can be varied and there are no fixed costs

Long-run production costs are influenced by economies of scale If IRTS, then costs increase at a decreasing rate If CRTS, then costs increase at a constant rate If DRTS, then costs increase at an increasing rate

We can calculate Long-run marginal cost (LRMC) Long-run average cost (LRAC), which is u-

shaped, reflecting the different stages of economies of scale

Long run production costs

In the short-run, total cost function is the following:TC = PKK0 + w*L = TFC + TVC

where the capital stock is fixed while the labor input is variable Example: David was a computer programmer at the

ICM and earned $120,000 per year. Now David has established his own consultancy. His monthly fixed costs, including rent, property, casualty and health insurance are $5,000. David’s monthly variable cost includes wages/salaries, telephone, maintenance, office supplies, internet , ... , and total $20,000.

Production costs (cont.)

Assuming that David does not pay himself a salary, what are the total monthly explicit costs?

What are the firm’s explicit monthly economic costs?

Production costs (cont.)

Duality of firm’s optimization problem: Minimizing PKK + wL subject to g(K, L)] ≥

Q* Maximize g(K, L)] subject to PKK + wL ≤ c* Both lead to the same first-order

conditions except for the Lagrangian (λ; measures the impact on the objective when the constraint is relaxed)

Write the Lagrangian equation for both and solve it!

Production costs (cont.)

Short- and long-run cost (cont.)

While the short-run average cost curves are derived from the law of diminishing returns, the long-run cost curve gets its shape from return to scale, characterized by the underlying long-run production function

The shape of the long-run average cost curve varies by industry (due to variations in return to scale)

There is no a priori reason to assume that the LRATC is u-shaped (e.g., CRTS has a horizontal LRATC curve)

Minimum efficient scale (MES) is the lowest per unit cost of production in the long-run

Short- and long-run cost (cont.)

In the short run firm should continue producing as long as price exceeds average variable cost (P > AVC)

In the long run firm has to cover all costs Hence it should continue to operation only if it expects

to earn positive economic profit in the long run A firm suffering persistent economic losses should

close Example. Firm’s cost function is C = 270 + 30Q +

0.3Q2. It faces demand P = 50 – 0.2Q. What is optimal level of Q in the short and long run?

The same principle applies to multiple production cases, i.e., each product should have a positive contribution to the firm’s profits

Short- and long-run cost (cont.)

Suppose a firm produces two goods: Q1 and Q2 Total fixed cost is $2.4 million per year Prices of goods are P1 = $10.00 and P2 = $6.50 Average variable costs are AVC1 = $9.00 and

AVC2 = $4.00 Let us assume that Q1 = 1.2 million and Q2 =

0.6 million Is it profitable to produce both goods in the

short and long run? What if P2 falls to $5.50? What if P2 falls to 3.50?

Short- and long-run cost (cont.)

Economies of scope exist when the total cost of using the same production facility to produce two or more goods is less than that of producing these goods at separate facilities

TC (Q1, 0) + TC(0, Q2) > TC(Q1, Q2) Example: It may be less expensive for Ford

Motor Company to produce cars and trucks using a single assembly line than do it in two separate facilities

Cost complementarities exist when MC of Q1 is lowered by increasing the production of Q2

Economies of scope

Example. A company produces two products (SUVs and light trucks) in the same manufacturing plant

Its costs are described by the following function:TC(Q1, Q2) = 25 + Q12 + 4*Q22 + 5*Q1*Q2

Calculate AC and MC for each product? Do cost complementarities exist? Discuss economies of scope for the firm. If the firm sells its division producing Q1, how

much it will cost to produce 10 units of Q2? What is the total cost of producing 5 units of Q1

and 10 units of Q2 after divesture?

Economies of scope (cont.)

Learning in industry means that as the production volume increases the unit cost of production falls

As more times a task has been performed, the less time it requires on each subsequent iteration

Reasons for learning effect Over time labor learns to do things more efficiently Better use of equipment, changes in input mix Product redesign

Arithmetic approach: each time production doubles, labor per unit declines by a constant (learning) factor

E.g., 1st unit requires 100 hours. If learning factor is 0.8, 2nd unit requires 80 hours, 3rd unit 64 hours, ….

Learning effect

The firm produces a single product or service The firm services a single market Its objective is to maximize profit The task is to determine how much to produce

and at what price to sell There is no uncertainty Let us assume that the demand is declining in

priceQ = 8.5 – 0.05*P

Draw the demand curve Rearrange as follows: P = 170 – 20* Q This is the firm’s “inverse demand equation”

Example of firm’s decisions

Total revenue of the firm is given by:P*Q = 170*Q – 20*Q2

Question to ask is what level of output maximizes the firm’s revenues?

d(P*Q)/dQ = 170 – 40*Q = 0Q* = 170/40 = 4.25 = 4 units

What is the shape of the revenue function? There is, however, costs associated with

production Let us assume that C = 100 + 38*Q

where 100 = fixed cost (unrelated to Q) 38 = variable cost (related to Q)

Example (cont.)

We see that total costs (C) is linear, rising function of Q

Profit is the difference between revenues and costs In this example, total profits (π) can be written as

π = P*Q – C = 170*Q – 20*Q2 - (100 + 38*Q) Maximization of profits with respect to Q means

dπ/dQ = 170 – 40*Q – 38 = 0Q* = (170 – 38)/40 = 132/40 = 3.3 = 3 units

Taking into account production costs, it is optimal for the firm to produce 3 units

Profits = P*Q – C = (170 – 20*3)* 3 – (100 – 38*3) = 330 – 100 – 114 = 116

Example (cont.)

We have assumed full certainty about the parameter of the example

In reality, however, conditions can changes Sensitivity analysis helps assess the impact of

changes in the key parameters Increased overhead/fixed costs, rising from 100

to 112 Increased material costs, rising from 38 to 46 Increased demand. The new demand is given byQ = 10 – 0.05* P

How would production and profits be affected by these changes?

Sensitivity analysis

Let’s us further assume that one-half of the demand is coming from abroad

What implications will this have? How would changes in the exchange rate

would affect firm’s production decision? What about having a portion of inputs

imported from abroad? How would depreciation of the U.S. dollar

against the foreign currency (say, the Euro) affect the producer’s output, sales at home and abroad, and profitability?

Sensitivity analysis (cont.)