Chapter 4

Question 1

Total Production Costs

Answer 1

= FC + VC

Fixed Costs + Variable Costs

Question 2

Total Fixed Costs

Answer 2

Costs that don’t vary with time or quantity

Question 3

Total Variable Costs

Answer 3

Costs that very with time or quantity

Question 4

Break-Even Rate

Answer 4

Production rate at which total costs = total revenue = 0

“Rate” being “number of units being produced”

Question 5

Theory of the Business Firm (and its 3 assumptions)

Answer 5

“In a process that produces goods or services.
Theory’s about finding the break-even rate, and maximizing total revenue.
Assumptions made:
- Unlimited resources (growth/process can continue indefinitely)
- Perfect market market competition (prices unaffected by individuals’ production choices, and are determined by supply and demand alone)
- Variables are exactly known for present and future periods.

Question 6

Average Cost

Marginal Cost

Answer 6

TC/Q
d(TC)/dQ

The total money spent in producing that one unit.

The instantaneous increase in cost if you produce one more unit.
( = vc for linear functions

Question 7

Average Fixed Cost

Average Variable Cost

Answer 7

fc = FC/Q
vc = VC/Q
The fixed-cost (or variable-cost) portion of the average cost.
Lowercase indicates an average value. **important for break-even analysis

Question 8

Cost Function
Revenue Function
(And the one assumption they make)

Answer 8

Functions of quantity (f(Q)) that tell you your total cost and your total revenue (assuming you sell everything you make and that there is perfect competition in the market, i.e. the rate of production does not affect the selling price)

Question 9

Contribution Margin

Answer 9

When you set TR = TC
(pQ = FC + vcQ)
Isolate for Q; this allows you to easily find the break-even rate.
The contribution margin is the denominator.
(p - vc)

More abstractly, it’s the portion of sales revenue that pays for the fixed costs.

Question 10

LAST CARD! :) Things to note:

Answer 10

Slides had a lot of examples on non-linear functions, finding max and min, inflection points, relating them to profit, minimizing project costs, etc.

Question 11

Quickly describe the graph obtained from plotting total TR and TC vs rate (linear cost functions)

Answer 11

Two linear functions where TR begins at the origin and TC begins above the origin. TR has a steeper slope than TC. The point of intersection is at rate = Q* (Break even rate)

Question 12

What does break even rate reflect about an operation?

Answer 12

Flexibility: High B/E rate = inflexible operation, while low B/E = more flexible operation, is more desirable.

Question 13

How can costs be lowered in an inefficient operation?

Answer 13

FC and vc can both be sometimes lowered

Question 14

How can the contribution margin be changed in an efficient operation?

Answer 14

Reducing the FC by shifting some of the fixed resources to variable resources (vc increases). This causes the contribution margin ( p - vc) to decrease.

Question 15

What are the benefits of a lower contribution margin?

Answer 15

Can lower the break-even rate and thus make for a more efficient operation. In other words, it can lower the portion of sales revenue used to pay off fixed costs and free more revenue for profit/ reinvestment/etc.

Question 16

What is a generalized cost function?

Answer 16

Cost function that assumes a portion, or all, of the variable inputs have non-liner behaviour with respect to production rate (in other words, vc depends on Q.) This is a more realistic assumption and leads to an s-shaped curve.

Question 17

What is the general format of a generalized cost function (s-shaped curve)?

Answer 17

TC = FC + (a)(Q) - (b)(Q^2) + (c)(Q^3)
Variable costs are represented by (a)(Q) - (b)(Q^2) + (c)(Q^3)
a, b and c are scaling constants.

Question 18

Average cost function (from s -shaped generalized cost function)

Answer 18

AC = TC/Q = FC/Q + a - (b)(Q)+(c)(Q^2)

Question 19

Marginal cost function (from s-shaped generalized cost function)

Answer 19

MC =dTC/dQ = a - (2b)(Q) + (3c)(Q^2)

Question 20

How can the minimum AC be found on a graph?

Answer 20

Is located at the point of tangency from the TC curve of a ray passing through the origin.
Is the most efficient use of fixed and variable resources

Question 21

How can the minimum MC be found on a graph?

Answer 21

Point of inflection of the TC function: where the slope of the TC function is at its minimum.

Question 22

Equation for the typical cost function used in design systems

Answer 22

TC = FC + (a)(S^b)
Where a and b are scaling constants and S = size

If b> 1 the TC function has positive inflection - there is a minimum AC.
Represents “Diseconomies of scale” : larger does not mean lower average costs.

If b = 1 TC is linear: the minimum AC is at infinity

If b < 1 TC has negative inflection: minimum AC is at infinity. Represents “Economies of scale” ; larger = lower average cost.

Question 23

How can the maximum total annual profit be found from a graph?

Answer 23

Point at which MR=MC (MP = MR-MC = 0)
In other words, the slope of the profit curve = 0 and is at a maximum. Can also be found from the equation MR=MC, isolating for Q.

Question 24

List 3 types of project cost components

Answer 24

1. Components for which costs are proportional to project size or variables
2. Components for which costs are inversely proportional to project size to variables
3. Components for which costs are constant over a particular range of project wives or variables.

Question 25

What generalized total cost function is generally used for minimization of project costs?

Answer 25

TC = a(S) + b/(S) + c where S = project size or variable a is the scaling component for proportional costs b is the scaling component for inversely proportional costs c represents constant costs.

Question 26

How can minimum costs (and the corresponding size/variable) be found using this function?

Answer 26

Solve dTC/dS = 0 for S