PRODUCTION AND COSTS:FIRM COSTS

AP Economics

Mr. Bordelon

Cost Curves• Fixed cost. Cost that does not depend on the quantity of

output produced. It is the cost of the fixed input.• Variable cost. Cost that depends on the quantity of

output produced. It is the cost of the variable input.• Total cost. Total cost of producing a given quantity of

output is the sum of the fixed cost and the variable cost of producing that quantity of output.• TC = FC + VC

• Total cost curve. Shows how total cost depends on quantity of output.

Total Cost Curve

Total Cost Curve

This table shows GM Farms’ total cost curve from the sum of their variable cost and their fixed costs.

In order to transform information from the production function to total cost, we need to know how much George and Martha pay for inputs.

For our purposes here, we’re assuming that George and Martha have a fixed cost of $400 for the use of the land. They will pay $400 whether they grow one bushel or 100.

Sometimes shows up on AP Exam (and in real life) as “overhead cost.”

Total Cost Curve

Additionally, we will assume that George and Martha must pay $200 for each worker. George and Martha know that the number of workers they must hire depends on the amount of wheat they intend to produce.

The cost of labor equals the number of workers times $200. This is the variable cost. Where are we getting the quantity of bushels from (on the x-axis)?

Adding VC and FC gives us TC, which can be graphed out.

Total Cost Curve

Total cost curve slopes upward, like the total product curve. Due to the increasing variable cost, the more output produced, the higher the farm’s total cost.

However, the total cost curve gets steeper. The slope of the total cost curve is greater as the amount of output produced increases.

What is ultimately causing this curve to slope upward? HINT: same thing that causes the total product curve to slope downward.

Total Cost Curve

Total cost curve slopes upward, like the total product curve. Due to the increasing variable cost, the more output produced, the higher the farm’s total cost.

However, the total cost curve gets steeper. The slope of the total cost curve is greater as the amount of output produced increases.

The slope of the total cost curve is due to diminishing returns on the variable input.

Marginal Cost• Marginal cost. Added cost of doing something one more

time. Change in total cost generated by producing one more unit of output.• MC = ΔTC/ΔQ

Marginal Cost

Marginal Cost

Marginal Cost

Marginal Cost

Marginal cost is equal to the slope of the total cost curve.

What was the slope of the total product curve?

Marginal Cost

Marginal cost is equal to the slope of the total cost curve.

Marginal product is equal to the slope of the total product curve.

In this case, this is the total cost curve of Selena’s Gourmet salsas, plotted out according to the table.

Marginal Cost

Marginal cost at Selena’s Gourmet Salsas rises as output increases. And because marginal cost equals the slope of the total cost curve, a higher marginal cost means a steeper slope.

Why does the marginal cost curve slope upward?

Marginal Cost

Marginal cost at Selena’s Gourmet Salsas rises as output increases. And because marginal cost equals the slope of the total cost curve, a higher marginal cost means a steeper slope.

The marginal cost curve slopes upward because there are diminishing returns to inputs.

As output increases, the marginal product of the variable input declines. More and more of the variable input must be used to produce each additional unit.

Since each additional variable unit must be paid for, the additional cost per additional unit also increases! Sexy, sexy.

Marginal Cost

The flattening of the total product curve as output increases and the steepening of the total cost curve as output increases are just flip-sides of the same coin.

As output increases, the marginal cost of output also increases because the marginal product of the variable input decreases.

Marginal Cost

Diminishing marginal returns•Total product curve. If quantities of other inputs are fixed, marginal product of an input falls as more of that variable input is used.•Total cost curve. If quantities of other inputs are fixed, marginal cost of output increases as more of that variable input is used (marginal product of the variable input decreases).

Average Total Cost• Average total cost. Total cost divided by quantity of

output produced.• ATC = TC/Q

• ATC tells producer how much the average unit of output costs to produce.• Contrast: marginal cost tells producer how much one more unit of

output costs to produce.

Average Total Cost

What happens to ATC as the quantity of output increases?

Average Total Cost Curve

ATC Curve

Drag picture to placeholder or click icon to addThis is the curve according to the data plotted in the average cost table for Selena’s Gourmet salsas. Notice the distinctive U-shape. Think of it as a warm economic hug. It reflects how ATC first falls and then rises as output increases.

But why does it do that?

Well...you’ll need to take a look at average fixed costs and average variable costs.

Take a deep breath.

Average Fixed and Variable Costs• Average fixed cost (AFC). Fixed cost divided by

quantity of output.• AFC = FC/Q

• Average variable cost (AVC). Variable cost divided by quantity of output.• AVC = FC/Q

AFC/AVC/ATC

AFC/AVC/ATCATC is the sum of the AFC and AVC. It has that economic hug because AFC and AVC move in opposite directions as output increases.

Math: AFC decreases as more output is produced because FC (numerator) is a fixed number but Q (denominator) increases as more is produced.

SS: As we produce more, our FC get spread out over more units produced. AFC will drop as we make more.

AFC/AVC/ATCMath: AVC increases as output increases.

SS: Each additional unit of output adds more to VC because increasing amounts of variable input are required to make another unit. We’re going to make need more stuff than we needed before to keep making products.

Spreading effect. Larger the output, greater quantity of output over which FC is spread, leading to lower AFC.

Diminishing returns effect. Larger the output, the greater the amount of variable input required to produce additional units, leading to higher AVC.

AFC/AVC/ATCAt low levels of output, spreading effect is more powerful because even small increases in output cause large reduction in AFC. At low levels of output, spreading effect dominates diminishing returns effect and causes ATC to slope downward.

At high levels of output, AFC is already small, so increasing output only has a small spreading effect.

AFC/AVC/ATCDiminishing returns grow more as output increases.

When output is large, diminishing returns effect dominates spreading effect, causing ATC to slope upward.

At the bottom of the economic hug ATC, point M, the two effects exactly balance each other out.

At point M, ATC is at its minimum level, the minimum ATC. It’s no coincidence that this is also the point where ATC = MC.

AFC/AVC/ATC Summary

Marginal cost curves slope upward. Diminishing returns that make an additional unit of output more costly to produce than the one before.

AVC curve slopes upward. Diminishing returns, but flatter than MC curve. Higher cost of an additional unit of output is averaged across all units, not just the additional unit.

AFC slopes downward. Spreading effect—larger the output, greater quantity of output over which FC is spread, leading to lower AFC.

AFC/AVC/ATC Summary

ATC slopes downward initially, then upwards. At low levels of output, spreading effect dominates diminishing returns effect and causes ATC to slope downward.

When output is large, diminishing returns effect dominates spreading effect, causing ATC to slope upward.

At the bottom of the economic hug ATC, point M, the two effects exactly balance each other out.

Marginal cost intersects ATC crossing at minimum ATC. Lowest point. At point M, ATC is at its minimum level, the minimum ATC.

ATC = MC.

Minimum Average Total Cost• Minimum-cost output. Quantity of output at which ATC

is at its lowest. Corresponds to the bottom of the U-shaped ATC curve.

• Why might this be important?

Minimum Average Total Cost• Minimum-cost output. Quantity of output at which ATC

is at its lowest. Corresponds to the bottom of the U-shaped ATC curve.

• Minimum-cost output gives producers an idea of just how much they can produce at the lowest cost possible.

Minimum ATC• The bottom of the U is at the level of output where MC

curve crosses the ATC curve.

1. At minimum-cost output, ATC is equal to MC.

2. When output is less than minimum-cost output, MC is less than ATC and ATC is decreasing.

3. When output is more than minimum-cost output, MC is greater than ATC and ATC is increasing.

Minimum ATC

1. ATC = MC (point M)

When MC equals ATC, at the bottom of the ATC curve because only there is ATC neither increasing or decreasing.

Minimum ATC2. MC < ATC, ATC decreasing. If

MC < ATC, producing the extra unit lowers ATC.(A1 to A2)

MC of producing an additional unit of output is low (MCL on MC curve).

When MC of producing next unit of output is less than ATC, increasing production reduces ATC.

Any quantity at which MC is less than ATC must be on the downward sloping segment of the ATC curve.

Minimum ATC

3. MC > ATC, ATC increasing. If MC > ATC, producing the extra unit raises ATC. (B1 to B2)

MC of producing an additional unit of output is high (MCH on MC curve).

When MC of producing next unit of output is more than ATC, increasing production increases ATC.

Any quantity of output where MC is more than ATC must be on the upward sloping segment of the ATC.

MC Curve Slope

• Diminishing returns lead to a marginal product curve that always slopes downward and a marginal cost curve that always slopes upward.

• In reality, economists believe that marginal cost curves slope downward as a firm increases its production from zero up to some low level, sloping upward only at higher levels of production.

MC Curve Slope

• The initial downward slope happens because a firm finds that when it starts with only a very small number of workers, employing more workers and expanding output allows workers to specialize. This, in turn, lowers the firm’s MC at it expands output.

MC Curve Slope

• Specialization leads to increasing returns to the hiring of additional workers, and leads to a MC curve that initially slopes downward.

• Once specialization is exhausted, diminishing returns to labor set in and the MC curve changes direction and slopes upward.

MC Curve Slope

• In any case, we see the same patterns as before:• ATC is U-shaped• MC curve passes

through point of minimum ATC

Bob’s Lemonade Stand• Bob has done an exhaustive study on the costs of producing cups of

lemonade, as he is wont to do. He must pay $50 every day to the city for the right to sell lemonade. This is a fixed cost because it doesn’t matter if he sells 50 cups or zero. He must also pay $25 for every employee he hires. This is his variable input (and thus, his variable cost).

Units of Labor Total Product (# of

cups/hour)

Variable Cost (VC)

Fixed Cost (FC)

Total Cost (TC = FC + VC)

0 0 $0 $50 $50

1 8 $25 $50 75

2 18 50 $50 100

3 26 75 $50 125

4 32 100 $50 150

5 36 125 $50 175

6 38 150 $50 200

Bob’s Lemonade Stand

• FC in this case is relatively horizontal. Notice the cost is paid even when zero cups of lemonade are produced.

• VC rises as more output is produced and begins to rise more and more quickly at higher levels of output.

• TC has the same shape as VC because it is simply VC plus a constant level of FC. The vertical distance between TC and VC is always FC ($50).

Bob’s Lemonade Stand• MC = ΔTC/ΔQ = Δ(VC + FC)/ΔQ = ΔVC/ΔQ• Marginal cost is the slope of total cost or variable cost.• The following table shows MC for the lemonade stand.

Notice that the change in output is in 8 units (this affects MC calculation).

Output MC ATC AVC AFC

8 3.13

18 2.50

26 3.13

32 4.17

36 6.25

38 12.50

Bob’s Lemonade Stand• Diminishing returns. MC initially

declines, but eventually increases as more output is produced. Diminishing returns to labor in production function cause this.

• As output increases, marginal product of variable input (labor) decreases. More and more labor must be used to produce each additional unit of output.

• Since each unit of labor must be paid for, the additional cost per additional unit of output also increases.

Output MC ATC AVC AFC

8 3.13

18 2.50

26 3.13

32 4.17

36 6.25

38 12.50

Bob’s Lemonade Stand

• ATC. ATC = TC/Q• AP additional terms:

average cost, unit cost, per unit cost.

• AVC. AVC = VC/Q• AFC. AFC = FC/Q

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• AFC. Decreases as more output is produced. FC is constant, but Bob is dividing by more and more cups of lemonade. He must pay $50 for the sidewalk, so when he divides by more cups of lemonade, FC is spread out over more output.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• AVC. As output increases, and diminishing returns becomes a major issue, the upward pull of AVC becomes stronger and begins to pull ATC upward.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• ATC. Initially declines, but eventually increases as more output is produced.

When more output is produced, the spreading effect lowers ATC as more output is produced.

When more output is produced, the diminishing returns effect causes ATC to increase.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• Spreading effect. Larger the output, the greater the quantity of output over which FC is spread, leading to lower AFC.

• Diminishing returns effect. Larger the output, the greater the amount of variable input required to produce additional units, leading to higher AVC.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• At low levels of output, the spreading effect is very powerful because even small increases in output cause large decreases in AFC, and pulls down ATC.

• As output increases, and diminishing returns becomes a major issue, the upward pull of AVC becomes stronger and pulls ATC upward.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• MC curve intersects ATC and AVC at their respective minimum points.

Output MC ATC AVC AFC

8 3.13 9.38 3.13 6.25

18 2.50 5.56 2.80 2.78

26 3.13 4.81 2.88 1.92

32 4.17 4.69 3.13 1.56

36 6.25 4.86 3.47 1.39

38 12.50 5.26 3.95 1.32

Bob’s Lemonade Stand

• Minimum ATC• ATC decreases as long as MC < ATC.• As MC increases, so that MC > ATC, ATC will increase.• If MC of next unit is equal to ATC, ATC will not change.

• Another example: GPA• If overall GPA is 3.0, and student earns a 4.0, overall GPA will

increase.• If overall GPA is 3.0, and student earns a 3.0, overall GPA will stay

the same.• If overall GPA is 3.0, and student earns a 2.0, overall GPA will

decrease.

Bob’s Lemonade Stand

• Looking at the MC curve for the lemonade stand shows that the MC initially decreases.

Bob’s Lemonade Stand

• MC can initially decrease due to specialization of labor in the production function.

• Before diminishing returns happens, imagine Bob divides up the tasks according to certain talents.

Bob’s Lemonade Stand

• Bob is great with customers, so she sells the lemonade, greets customers, etc.

• Bobbette, Bob’s employee, is extremely fast in the kitchen, squeezing lemons, mixing sugar, and dreaming of lemon cupcakes.

• With this kind of specialization, marginal product increases.

• However, when Bob hires Bobb, Bobby, and Bobberino McBobster, diminishing returns are experienced, and MC increases.