4 -- Case Study- Economic for Strategic decision

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MBA 681 Economics for Strategic Decisions Prepared by Yun Wang

Outline

1 Production 2 The Short Run and the Long Run in Economics 3 The Marginal Product of Labor and the Average Product of Labor 4 The Relationship between Short-Run Production and Short-Run Cost 5 Graphing Cost Curves 6 Costs in the Long Run Appendix: using Isoquants and Isocost lines to understand production and cost

1 What Owners Want

• We focus on for-profit firms in the private sector in this course. • We assume these firms’ owners are driven to maximize profit.

• Profit is the difference between revenue (R), what it earns from selling its product, and cost (C), what it pays for labor, materials, and other inputs.

where R = pq. • To maximize profits, a firm must produce as efficiently as possible, where

efficient production means it cannot produce its current level of output with fewer inputs.

1 Production

• The various ways that a firm can transform inputs into the maximum amount of output are summarized in the production function.

• Assuming labor (L) and capital (K) are the only inputs, the production function is .

• A firm can more easily adjust its inputs in the long run than in the short run.

• The short run is a period of time so brief that at least one factor of production cannot be varied (the fixed input).

• The long run is a long enough period of time that all inputs can be varied.

6.3 Short Run Production: One Variable and One Fixed Input

• In the short run (SR), we assume that capital is a fixed input and labor is a variable input.

• SR Production Function: • q is output, but also called total product; the short run production

function is also called the total product of labor • The marginal product of labor is the additional output produced by an

additional unit of labor, holding all other factors constant.

• The average product of labor is the ratio of output to the amount of labor employed.

Table 1 Short-Run Production and Cost at Jill Johnson’s Restaurant (1 of 3)

Quantity of Workers

Quantity of Pizza Ovens

Quantity of Pizzas per

Week

Cost of Pizza Ovens (Fixed

Cost)

Cost of Workers

(Variable Cost)

Total Cost of Pizzas per Week

Cost per Pizza (Average Total

Cost) 0 2 0 $800 $0 $800 — 1 2 200 800 650 1,450 $7.25 2 2 450 800 1,300 2,100 4.67 3 2 550 800 1,950 2,750 5.00 4 2 600 800 2,600 3,400 5.67 5 2 625 800 3,250 4,050 6.48 6 2 640 800 3,900 4,700 7.34

Jill Johnson’s restaurant has a particular technology by which it transforms workers and pizza ovens into pizzas. • With more workers, Jill can produce more pizzas.

This is the firm’s production function: the relationship between the inputs employed and the maximum output from those inputs.

Table 1 Short-Run Production and Cost at Jill Johnson’s Restaurant (2 of 3)

Quantity of Workers

Quantity of Pizza Ovens

Quantity of Pizzas per

Week

Cost of Pizza Ovens (Fixed

Cost)

Cost of Workers

(Variable Cost)

Total Cost of Pizzas per Week

Cost per Pizza (Average Total

Cost)

0 2 0 $800 $0 $800 —

1 2 200 800 650 1,450 $7.25

2 2 450 800 1,300 2,100 4.67

3 2 550 800 1,950 2,750 5.00

4 2 600 800 2,600 3,400 5.67

5 2 625 800 3,250 4,050 6.48

6 2 640 800 3,900 4,700 7.34

Each pizza oven costs $400 per week, and each worker costs $650 per week. • So the firm has $800 in fixed costs, and its costs go up $650 for

each worker employed.

Figure 1 Graphing Total Cost and Average Total Cost at Jill Johnson’s Restaurant (1 of 2) Using the information from the table, we can graph the costs for Jill Johnson’s restaurant.

Notice that cost is not zero when quantity is zero, because of the fixed cost of the pizza ovens.

Naturally, costs increase as Jill wants to make more pizzas.

Table 1 Short-Run Production and Cost at Jill Johnson’s Restaurant (3 of 3)

Quantity of Workers

Quantity of Pizza Ovens

Quantity of Pizzas per

Week

Cost of Pizza Ovens (Fixed

Cost)

Cost of Workers

(Variable Cost)

Total Cost of Pizzas per Week

Cost per Pizza (Average Total

Cost)

0 2 0 $800 $0 $800 —

1 2 200 800 650 1,450 $7.25

2 2 450 800 1,300 2,100 4.67

3 2 550 800 1,950 2,750 5.00

4 2 600 800 2,600 3,400 5.67

5 2 625 800 3,250 4,050 6.48

6 2 640 800 3,900 4,700 7.34

If we divide the total cost of the pizzas by the number of pizzas, we get the average total cost of the pizzas.

For low levels of production, the average cost falls as the number of pizzas rises; at higher levels, the average cost rises as the number of pizzas rises.

Figure 1 Graphing Total Cost and Average Total Cost at Jill Johnson’s Restaurant (2 of 2) The “falling-then-rising” nature of average total costs results in a U-shaped average total cost curve.

Our next task is to examine why we get this shape for average total costs.

3 The Marginal Product of Labor and the Average Product of Labor Understand the relationship between the marginal product of labor and the average product of labor.

Suppose Jill Johnson hires just one worker; what does that worker have to do? • Take orders • Make and cook the pizzas • Take pizzas to the tables • Run the cash register, etc.

By hiring another worker, these tasks could be divided up, allowing for some specialization to take place, resulting from the division of labor.

Two workers can probably produce more output per worker than one worker can alone.

Table 2 The Marginal Product of Labor at Jill Johnson’s Restaurant (1 of 2)

Quantity of Workers

Quantity of Pizza Ovens

Quantity of Pizzas

Marginal Product of Labor

0 2 0 — 1 2 200 200 2 2 450 250 3 2 550 100 4 2 600 50 5 2 625 25 6 2 640 15

Let’s examine what happens as Jill Johnson hires more workers.

To think about this, consider the marginal product of labor: the additional output a firm produces as a result of hiring one more worker. • The first worker increases output by 200 pizzas; the second increases

output by 250.

Table 2 The Marginal Product of Labor at Jill Johnson’s Restaurant (2 of 2) Additional workers add to the potential output but not by as much. Eventually they start getting in each other’s way, etc., because there is only a fixed number of pizza ovens, cash registers, etc.

Law of diminishing returns: At some point, adding more of a variable input, such as labor, to the same amount of a fixed input, such as capital, will cause the marginal product of the variable input to decline.

Figure 2 Total Output and the Marginal Product of Labor Graphing the output and marginal product against the number of workers allows us to see the law of diminishing returns more clearly.

The output curve flattening out, and the decreasing marginal product curve, both illustrate the law of diminishing returns.

Average Product of Labor Another useful indication of output is the average product of labor, calculated as the total output produced by a firm divided by the quantity of workers. • With 3 workers, the restaurant can produce 550 pizzas, giving an

average product of labor of: 550 183.3

3 

A useful way to think about this is that the average product of labor is the average of the marginal products of labor. • The first three workers give 200, 250, and 100 additional pizzas

respectively:

200 250 100 183.3 3

  

Average and Marginal Product of Labor With only two workers, the average product of labor was:

200 250 450 225 2 2 

 

So the third worker made the average product of labor go down. • This happened because the third worker produced less (marginal)

output than the average of the previous workers.

If the next worker produces more (marginal) output than the average, then the average product will rise instead. • The next slide illustrates this idea using college grade point averages

(GPAs).

Figure 3 Marginal and Average GPAs Paul’s semester GPA starts off poorly, rises, then eventually falls in his senior year.

His cumulative GPA follows his semester GPA upward, as long as the semester GPA is higher than the cumulative GPA.

When his semester GPA dips down below the cumulative GPA, the cumulative GPA starts to head down also.

4 The Relationship between Short-Run Production and Short-Run Cost Explain and illustrate the relationship between marginal cost and average total cost. We have already seen the average total cost: total cost divided by output.

We can also define the marginal cost as the change in a firm’s total cost from producing one more unit of a good or service:

TCMC Q

 



Sometimes 1,Q  so we can ignore the bottom line, but don’t get in the habit of doing that, or you’ll make mistakes when quantity changes by more than 1 unit.

Figure 4 Jill Johnson’s Marginal Cost and Average Cost of Producing Pizzas We can visualize the average and marginal costs of production with a graph.

The first two workers increase average production and cause cost per unit to fall; the next four workers are less productive, resulting in high marginal costs of production.

Since the average cost of production “follows” the marginal cost down and then up, this generates a U-shaped average cost curve.

Quantity of Workers

Quantity of Pizzas

Marginal Product of Labor

Total Cost of Pizzas

Marginal Cost of Pizzas

Average Total Cost of Pizzas

0 0 – $800 – – 1 200 200 1,450 $3.25 $7.25 2 450 250 2,100 2.60 4.67 3 550 100 2,750 6.50 5.00 4 600 50 3,400 13.00 5.67 5 625 25 4,050 26.00 6.48 6 640 15 4,700 43.33 7.34

5 Graphing Cost Curves Graph average total cost, average variable cost, average fixed cost, and marginal cost.

We know that total costs can be divided into fixed and variable costs: TC FC VC 

Dividing both sides by output (Q) gives a useful relationship: TC FC VC Q Q Q

 

• The first quantity is average total cost. • The second is average fixed cost: fixed cost divided by the quantity

of output produced. • The third is average variable cost: variable cost divided by the

quantity of output produced. So, ATC AFC AVC 

Figure 5 Costs at Jill Johnson’s Restaurant (1 of 2)

Quantity of workers

Quantity of ovens

Quantity of Pizzas

Cost of Ovens

(fixed cost)

Cost of workers

(variable cost) Total Cost of Pizzas ATC AFC AVC MC

0 2 0 $800 $0 $800 – – – – 1 2 200 800 650 1,450 $7.25 $4.00 $3.25 $3.25 2 2 450 800 1,300 2,100 4.67 1.78 2.89 2.60 3 2 550 800 1,950 2,750 5.00 1.45 3.54 6.50 4 2 600 800 2,600 3,400 5.67 1.33 4.33 13.00 5 2 625 800 3,250 4,050 6.48 1.28 5.20 26.00 6 2 640 800 3,250 4,050 6.48 1.28 5.20 26.00 6 2 640 800 3,900 4,700 7.34 1.25 6.09 43.33

Observe that: • In each row, ATC = AFC + AVC. • When MC is above ATC, ATC is falling. • When MC is above ATC, ATC is rising. • The same is true for MC and AVC.

Figure 5 Costs at Jill Johnson’s Restaurant (2 of 2) This results in both ATC and AVC having their U-shaped curves.

The MC curve cuts through each at its minimum point, since both ATC and AVC “follow” the MC curve.

Also notice that the vertical sum of the AVC and AFC curves is the ATC curve.

And because AFC gets smaller, the ATC and AVC curves converge.

6 Costs in the Long Run Understand how firms use the long-run average cost curve in their planning. Recall that the long run is a sufficiently long period of time that all costs are variable. • So In the long run, there is no distinction between fixed and variable

costs.

A long-run average cost curve shows the lowest cost at which a firm is able to produce a given quantity of output in the long run, when no inputs are fixed.

Figure 6 The Relationship between Short-Run Average Cost and Long-Run Average Cost (1 of 3) At low quantities, a firm might experience economies of scale: the firm’s long-run average costs falling as it increases the quantity of output it produces.

Here, a small car factory can produce at a lower average cost than a large one, for small quantities. For more output, a larger factory is more efficient.

Figure 6 The Relationship between Short-Run Average Cost and Long-Run Average Cost (2 of 3) The lowest level of output at which all economies of scale are exhausted is known as the minimum efficient scale. At some point, growing larger does not allow more economies of scale. The firm experiences constant returns to scale: its long- run average cost remains unchanged as it increases output.

Figure 6 The Relationship between Short-Run Average Cost and Long-Run Average Cost (3 of 3) Eventually, firms might get so large that they experience diseconomies of scale: a situation in which a firm’s long-run average costs rise as the firm increases output.

This might happen because the firm gets to large to manage effectively, or because the firm has to employ workers or other factors of production that are less well suited to production.

Long-Run Average Cost Curves for Automobile Factories Why might a car company experience economies of scale? • Production might increase at a greater than proportional rate as inputs

increase. • Having more workers can allow specialization. • Large firms may be able to purchase inputs at lower prices.

But economies of scale will not last forever. • Eventually managers may have difficulty coordinating huge operations.

“Demand for… high volumes saps your energy. Over a period of time, it eroded our focus… [and] thinned out the expertise and knowledge we painstakingly built up over the years.”

- President of Toyota’s Georgetown plant

Table 3 A Summary of Definitions of Cost

Term Definition Symbols and

Equations

Total cost The cost of all the inputs used by a firm, or fixed cost plus variable cost

Fixed costs Costs that remain constant as a firm’s level of output changes FC

Variable costs Costs that change as a firm’s level of output changes VC

Marginal cost An increase in total cost resulting from producing another unit of output

Average total cost Total cost divided by the quantity of output produced

Average fixed cost Fixed cost divided by the quantity of output produced

Average variable cost

Variable cost divided by the quantity of output produced

Implicit cost A nonmonetary opportunity cost — Explicit cost A cost that involves spending money —

TCMC Q

 



TCATC Q



FCAFC Q



VCAVC Q



Appendix: Using Isoquants and Isocost Lines to Understand Production and Cost Use isoquants and isocost lines to understand production and cost. Suppose a firm has determined it wants to produce a particular level of output. What determines the cost of that output? 1. Technology

In what ways can inputs be combined to produce output? 2. Input prices

What is the cost of each input compared with the other? That is, what is the relative price of each input?

Figure A.1 Isoquants (1 of 3) If a firm’s technology allows one input to be substituted for the other in order to maintain the same level of production, then many combinations of inputs may produce the same level of output.

The pizza restaurant might be able to produce 5,000 pizzas with either • 6 workers and 3 ovens; or • 10 workers and 2 ovens.

An isoquant is a curve showing all combinations of two inputs, such as capital and labor, that will produce the same level of output.

Figure A.1 Isoquants (2 of 3) More inputs would allow a higher level of production; with 12 workers and 4 ovens, the restaurant could produce 10,000 pizzas.

A new isoquant describes all combinations of inputs that could produce 10,000 pizzas.

Greater production would require more inputs.

Figure A.1 Isoquants (3 of 3) The slope of an isoquant describes how many units of capital are required to compensate for a unit of labor, keeping production constant. • This is the marginal rate of technical

substitution.

Between A and B, 1 oven can compensate for 4 workers; the

1MRTS 4



Additional workers are poorer and poorer substitutes for capital, due to diminishing returns; so the MRTS gets smaller as we move along the isoquant, giving a convex shape.

Figure A.2 An Isocost Line For a given cost, various combinations of inputs can be purchased.

The table shows combinations of ovens and workers that could be produced with $6,000, if ovens cost $1,000 and workers cost $500.

Isocost line: All the combinations of two inputs, such as capital and labor, that have the same total cost.

Combinations of Workers and Ovens with a Total Cost of $6,00

Point Ovens Workers Total Cost A 6 0 (6  $1,000) + (0  $500)= $6,000

B 5 2 (5  $1,000) + (2  $500)= $6,000

C 4 4 (4  $1,000) + (4  $500)= $6,000 D 3 6 (3  $1,000) + (6  $500)= $6,000 E 2 8 (2  $1,000) + ( 8  $500) = $6,000

F 1 10 (1  $1,000) +( 10  $500) = $6,000

G 0 12 (0  $1,000) + (12  $500) = $6,000

Figure A.3 The Position of the Isocost Line With more money, more inputs can be purchased.

The slope of the isocost line remains constant, because it is always equal to the price of the input on the horizontal axis divided by the price of the input on the vertical axis, multiplied by −1.

The slope indicates the rate at which prices allow one input to be traded for the other: here, 1 oven costs the same as 2 workers:

1slope 2

 

Figure A.4 Choosing Capital and Labor to Minimize Total Cost Suppose the restaurant wants to produce 5,000 pizzas. • Point B costs only $3,000 but

doesn’t produce 5000 pizzas. • Points A, C, and D all produce

5,000 pizzas. • Point A is the cheapest way to

produce 5,000 pizzas; the isocost line going through it is the lowest.

Observe that at this point, the slope of the isoquant and isocost line are equal.

Figure A.5 Changing Input Prices Affects the Cost-Minimizing Input Choice If prices change, so does the cost-minimizing combination of capital and labor.

Suppose we open a pizza franchise in China, where ovens are more expensive ($1,500) and workers are cheaper ($300). The isocost lines are now flatter.

To obtain the same level of production, we would substitute toward the input that is now relatively cheaper: workers.

Another Look at Cost Minimization We observed that at the minimum cost level of production, the slopes of the isocost line and the isoquant were equal.

Generally, writing labor as L and capital as K, we have:

Slope of isoquant MRTS Slope of isocost lineL K

P P

    

So at the cost-minimizing level of production, MRTS .L K

P P



• The MRTS tells us the rate at which a firm is able to substitute labor for capital, given existing technology.

• The slope of the isocost line tells us the rate at which a firm is able to substitute labor for capital, given current input prices.

• These are equal at the cost-minimizing level of production, but there is no reason they should be equal elsewhere.

Moving Along an Isoquant (1 of 2) Suppose we move between two points on an isoquant, increasing labor and decreasing the capital used.

When we increase labor, we increase production by the number of workers we add times their marginal production:

Change in quantity of workers LMP

We can interpret the reduction in output from reducing capital in the same way: it is equal to the amount of capital we remove, times the marginal production of that capital:

Change in quantity of capital KMP 

Moving Along an Isoquant (2 of 2) Since we are moving along an isoquant, production stays constant • So the decrease in output from using less capital must exactly equal

the increase in output from increasing labor:

Change in quantity of capital change in q uantity of workersK LMP MP   

Rearranging this equation gives:

Change in quantity of capital Change in the quantity of workers

MP MP

 

The left hand side is the slope of the isoquant: the MRTS. So:

MPMRTS MP



Optimality Condition for a Firm The slope of the isocost line is the wage rate (w) divided by the rental price of capital (r). Earlier in the appendix, we showed that at the cost-minimizing point,

wMRTS r



So now we know that at the cost-minimizing point:

MP w MP r



Rearranging gives us:

L KMP MP w r



Interpreting the Firm’s Optimality Condition L KMP MP

w r 

At the cost-minimizing input combination, the marginal output of the last dollar spent on labor should be equal to the marginal output of the last dollar spent on capital.

We could use this idea to determine whether a firm was producing efficiently or not: if an extra dollar spent on capital produced more (less) output than an extra dollar spent on labor, then the firm is not minimizing costs; it could: • increase (decrease) capital, and • decrease (increase) labor,

maintaining the same level of output and lowering cost.

Figure A.6 The Expansion Path (1 of 2) A bookcase manufacturing firm produces 75 bookcases a day, using 60 workers and 15 machines.

In the short run, if the firm wants to expand production to 100 bookcases, it must do so by employing more workers only; the number of machines is fixed.

Notice that there is are lower-cost combination of inputs (like point C) that would produce 100 bookcases; in the long run, the firm will switch to one of those.

Figure A.6 The Expansion Path (2 of 2) Point C is a combination on the long-run expansion path for the firm: a curve that shows the firm’s cost-minimizing combination of inputs for every level of output.

We can tell because the isocost line and isoquant are tangent at point C.

Point A minimizes costs for a lower quantity (50).

The expansion path is the set of all cost-minimizing bundles, given a particular set of input prices.