Download Chapter 7: The Theory and Estimation of Cost: Problems: Question

Chapter 7: The Theory and Estimation of Cost:
Problems:
Question (5) Decide whether the following is true or false and explain why?
[A] A decision maker must always use the historical cost of raw materials in making an
economic decision.
[False]
Historical costs are cost of items at the price originally paid for them, while replacement cost
valuation states the costs at the prices that would have to be paid currently. Costs reported
by conventional financial accounts are based on historical (original outlay) valuation.
In a business organization, management has to make plans for the future and also choose
between alternative plans. While making these choices, an estimate must be made how
each alternative plan will affect future expenses and revenues. Hence cost estimates must
be tailored to the economic characteristics of the choices. The only costs that matter for
business decisions are future costs; “actual” costs i.e., current or historical costs are useful
solely as a benchmark for estimating the costs that lie ahead if one course of action is
choose as opposed to another.
In doing this kind of managerial cost analysis, only those expenses and revenues which will
be affected by a decision should be considered; the expenses and revenues that remain the
same whatever be the plan chosen need not be considered at all.
[B] The marginal cost curve always intersects the average cost curve at the average cost's
lowest point.
[True]
Cost curves can be combined to provide information about firms (assuming in a perfectly
competitive market). The marginal cost curve will cut the average cost curve at its lowest
point. In this case, a firm's profit maximizing price would be at or above the price at which
the average cost curve cuts the marginal cost curve. If the marginal revenue is above the
average total cost price the firm is deriving an economic profit.
When the marginal cost is below the average total costs or the average variable costs, then
the Average Cost would be declining. When marginal cost is above the average cost then the
average cost would be increasing. Therefore the marginal cost should intersect with the
average cost at the lowest point in order to pull the average cost upwards.
[C] The portion of the long-run cost curve that is horizontal indicates that the firm is
experiencing neither economies nor diseconomies of scale.
[True]
Economies of scale are reductions in the firm's per-unit costs that are associated with the
use of large plants to produce a large volume of output. They are present over the initial
range of outputs when the long-run ATC curve is falling. There are three reasons why
economies of scale exist:
1. Mass production is more economical.
2. Specialization of labor and equipment improves productivity.
3. Workers at a larger firm tend to learn more from their experience.
Diseconomies of scale are situations in which the long-run average total costs are greater
firms than they are for smaller firms. They are possible: as a firm gets bigger and bigger,
bureaucratic inefficiencies may result. Principal-agent problems grow - they are present
when the long-run ATC curve is rising.
It is also possible to have constant unit costs as the plant size changes. This is known as
constant returns to scale.
Economies and diseconomies of scale are long-run concepts. They relate to conditions of
production when all factors are variable. In contrast, increase and diminishing returns are
short-run concepts, applicable only when the firm has a fixed factor of production.
The downward sloping portion shows economies of scale. The horizontal portion shows
constant returns to scale. The upward sloping portion shows diseconomies of scale.
[D] Marginal Cost is relevant only in the short-run analysis of the firm.
[False]
Marginal cost is the affect on total cost caused by a unit change in production. The total cost
is the summation of the variable costs (expenses that change with business activity--such as
material supplies) and fixed costs (expenses unrelated to business activity--such as rent).
Due to the complexity of market conditions and production, marginal cost is usually
examined in both the short term and long term.
To calculate marginal cost in the short term, you must keep the fixed costs as constant; they
must remain unchanged. The short-term calculation refers to changes in variable inputs,
such as labor and materials, and its affect on total cost.
When looking at a short-term marginal cost curve on a graph, notice how the curve is steep.
This is due to the affect of the law of diminishing marginal returns on the marginal cost
curve. The law of diminishing marginal returns states the point at which a decline in
production occurs as the factors of production increase.
In the long term, the fixed costs are not held constant. The graph of a long-term marginal
cost curve is much flatter than the short-term marginal cost curve. This is due to the fact
that the long-term curve is shaped by economies of scale. The principle of economies of
scale takes into account the cost benefits due to expansion that lead to an increase in
production. The producer wants the average cost per unit of production to decrease as the
scale, or number of inputs, increases.
[E] The Rational firm will try to operate most efficiently by producing at the point where its
average cost is minimized.
[True]
Average Cost (AC) is the sum of Average Fixed Cost (AFC) and Average Variable Cost (AVC).
As the production increases, average fixed cost goes on falling. In the initial stages of
production, average variable cost also goes on falling. Consequently, the sum of these two
costs (average cost) also falls and reaches its minimum point, as per the figure. Up to point
A, average cost curve is falling. It is at its minimum at point 'A'. In this situation, the firm is
making use of its production capacity. The firm is having optimum output. Optimum output
refers to that level of output which corresponds to the lowest per unit cost of production as
at point A in the figure.
If the firm produces beyond this point, no doubt, average fixed cost will continue to fall, but
average variable cost will begin to rise. Rising average variable cost makes the average cost
to rise also. It is so because after reaching its minimum level, rate of increase in average
variable cost is much more than rate of decrease in average fixed cost. The net effect is
reflected in the upward rising AC curve. In this way, average cost curve being the sum of
average fixed cost and average variable cost, initially falls and having reached its minimum
begin to rise.
Sue to the diminishing marginal productivity, marginal costs are typically increasing. An
increasing marginal cost curve will intersect the U-shaped average cost curve at its
minimum, after which point the average cost curve begins to slope upward.
Question (4): You are given the following cost functions:
TC =100 + 60Q- 3Q2 + 0.1Q3
TC =100 + 60Q+ 3Q2
TC = 100 + 60Q
a. Compute the average variable cost, average cost, and marginal cost for each
function.
Plot them on a graph.
b. In each case, indicate the point at which diminishing returns occur. Also indicate
the point of maximum cost efficiency (i.e., the point of minimum average cost).
c. For each function, discuss the relationship between marginal cost and average
variable cost and between marginal cost and average cost. Also discuss the
relationship between average variable cost and average cost.
Solution:
- For The Total Cost Function TC =100 + 60Q- 3Q2 + 0.1Q3
(a) The total fixed-cost component of this equation is simply the constant term = 100.
(b) The balance of the right-hand side gives us total variable cost 60Q - 3Q2 + 0.1Q3.
Average Fixed Cost (AFC) = TFC/Q = 100/Q
Average Variable Cost (AVC)
Average Total Cost (AC)
= TVC / Q
= (60Q – 3Q2 + 0.1.Q3) / Q
= 60 – 3 Q + 0.1 Q2
= TC/Q = 100/Q + 100/Q + 60 – 3 Q + 0.1 Q2
Marginal Cost (MC) = Delta TC / Delta Q
= Derivative of the total cost function (TC =100 + 60Q- 3Q2 + 0.1Q3)
= 60 – 6Q + 0.3Q2
Plot on Graph:
Q
TFC
TVC
TC
AFC
AVC
AC
MC
0
100
0
100
1
100
57.1
157.1
100
57.1
157.1
51.7
2
100
108.8
208.8
50
54.4
104.4
46.9
3
100
155.7
255.7
33.333333
51.9
85.233333
42.7
4
100
198.4
298.4
25
49.6
74.6
39.1
5
100
237.5
337.5
20
47.5
67.5
36.1
6
100
273.6
373.6
16.666667
45.6
62.266667
33.7
7
100
307.3
407.3
14.285714
43.9
58.185714
31.9
8
100
339.2
439.2
12.5
42.4
54.9
32.8
16
100
601.6
701.6
6.25
37.6
43.85
49.6
20
100
800
900
5
40
45
73.6
24
100
1094.4
1194.4
4.1666667
45.6
49.766667
117.6
30
100
1800
1900
3.3333333
60
63.333333
220
40
100
4000
4100
2.5
100
102.5
- For The Total Cost Function TC =100 + 60Q+ 3Q2
Average Variable Cost (AVC)
= TVC / Q
= (60Q + 3Q2) / Q
= 60 - 3Q
Average Total Cost (AC)
= TC/Q = 100/Q + 60 - 3Q
Marginal Cost (MC) = Delta TC / Delta Q
= Derivative of the total cost function (TC =100 + 60Q- 3Q2)
= 60 – 6Q
- For The Total Cost Function TC =100 + 60Q
Average Variable Cost (AVC)
= TVC / Q
= 60Q / Q
= 60
Average Total Cost (AC)
= TC/Q = 100/Q + 60
Marginal Cost (MC) = Delta TC / Delta Q
= Derivative of the total cost function (TC =100 + 60Q)
= 60
YOU CAN MAKE THE TABLE AND PLOT GRAPH FOR THE REST AS INDICATED ABOVE
(b)
- The Point of Maximum Cost efficiency is the point where the Average Cost is in its minimum. In the
case of formula 1, this point is when Q = 16
- The point where the diminishing returns occur is the point where the marginal cost started to go up.
In the case of formula 1, this point is when Q = 7
You can apply the same for the other two formulas.
(C)
Questions:
"If it were not for the law of diminishing returns, a firm's average cost and average
variable cost would not increase in the short run"
Do you agree with this statement? why?
Yes I totally agree. The law of diminishing returns simply means that as you add more of one
factor of production (keeping others constant), the additional increase in output you get
(marginal product) drops over time.
As Marginal Product falls over time, marginal cost increases (same wage, produce fewer
extra units means cost of these units is higher than the previous ones), and this drags up
average variable and average total costs.
Now if all workers contributed, the average cost would just keep on dropping.