Chapter 9: Cost
Short Answer Questions
1. Briefly outline the information conveyed in a short-run cost curve.
Answer: The short-run economic cost function measures the minimal level of total
expenditures (measured in opportunity cost terms) needed to produce a given amount
of output in the short run.
2. What is the relationship between short run marginal and average variable
costs?
Answer: The short run marginal cost curve crosses the short run average cost variable
cost at all points where average variable cost is in minimum.
3. Explain the term “isocost line” and “isocost map”.
Answer: An isocost line is a line that represents all input combinations that cost the
firm the same amount. An isocost map is a visualisation of the whole family of isocost
lines that exist for a given set of factor prices.
4. Define the term “output expansion path” and explain its use.
Answer: The term output expansion path refers to the long-run set of least-cost input
levels, traced out as the level of output changes, ceteris paribus.
5. Using an algebraic approach, briefly derive the condition that needs to hold for
the selected input mix to be efficient. Discuss your result.
Answer: The returns to the factors of production should just be equal to their marginal
products. See “Algebraic Interpretation” in section 9.2
For the remaining questions support your answers with the aid of appropriate
diagrams.
6. Discuss the relationship between the short-run marginal cost and the short-run
average variable cost.
Answer: Whenever marginal cost is below average variable cost, average variable
cost falls. And whenever marginal cost is above average variable cost, average
variable cost rises. As a result, the short-run marginal cost curve crosses the short-run
average variable cost curve at the point where the average variable cost is at a
minimum.
7. Assume that a firm uses only one factor of production (L), and that it is
characterised by a constant Marginal Physical Product (MPP). What can you
tell about the short run marginal ost curve for this firm?
Answer:
When the marginal physical product of labour is constant at m, each additional unit of
output requires 1/m additional units of labour. Because each labourer receives a wage
of w, short-run total cost rises by w/m. Hence, the short-run marginal cost is w/m at
every output level.
8. Discuss how a decrease in wage rate affects the isocost line.
Answer: When the price of labour decreases (that is, the wage rate decreases), the
isocost pivots outwards from IC to IC’.
9. Assume now that the same firm employs two factors of production, K and L,
initially paid at a rate r and w, respectively. Explain what will happen if the
wage rate for L increases and the firm want to keep the same level of
production as before. Show the new equilibrium point.
Answer:
When the price of labour rises, the isocost lines pivot inwards. To keep the same level
of output the firm has to increase its total cost of production. The new equilibrium
occurs at point e2 which is a result of the firm substitutes away from labour whose
price has increased.
10. Briefly explain how the development of a new, more efficient production
technology would affect the equilibrium output of a firm that uses this
technology.
Answer:
As a result of the technological improvement, the firm can continue to produce 200
cars per day while using fewer workers and robots. The isoquant shifts inward from
the x200 -isoquant to the x '200 -isoquant. The new equilibrium point is e3 and the total
cost of producing 200 cars per day falls by 10,000 per day.
Essay questions
1. A firm’s production depends on one single factor, labour. Initially the firm is
believed to be understaffed and its management decides that they can expand
their output capacity by hiring more workers (L). L’s returns are believed to be
variable and follow the “Law of Diminishing Returns”. Show in a diagram (if
everything else is being equal) how would you expect the marginal physical
product and short-run marginal cost curves to look like as the number of
workers employed by the firm changes.
Brief answer: The reader should discuss the meaning of the “Law of Diminishing
Returns” and explain that when there are diminishing marginal returns to labour,
increasingly large increments of labour are needed to produce additional output.
Consequently, the MPPL curve slopes downwards and the short-run marginal cost
curve slopes upwards as when MPPL falls the MCSR rises.
2. Discuss the concept of economically efficient input. Use examples to support
your answer.
Brief answer: An input combination is economically efficient when it has the lowest
opportunity cost of those input combinations that can be used to produce the desired
output. The input combination at point e1 is economically efficient because it
minimises the firm’s cost of producing the targeted level of output. At this point, the
slope of isoquants equals to the input prices ratio.
3. “To improve the quality of output, a firm would have to bear an increase in its
production cost. There is just no other way”. Do you agree with this
statement? Use diagrams to support your answer.
Brief answer: This may be the case if the only way for the firm to ensure a higher
quality level for its output is to devote more resources to the production of any given
level of output. For example, to produce the same number of cars, the firm (National
Motors) has to hire more engineering and more equipment to screen the assembly
line. As a result, the isoquant shifts outward and the new equilibrium point is e4. The
total cost of producing the same amount of cars per day increases.
4. A production technology can exhibit economies, diseconomies or no effect of
scale. Explain and compare.
Brief answer: The reader should first discuss the concept of economies of scale. We
observe economies of scale when long run average costs fall as output increases.
There exists the relationship between economies of scale and returns to scale of the
production function. When the production function exhibits constant returns to scale,
long-run average cost remains constant as the level of output changes. When the
production function exhibits decreasing returns to scale, the long-run total cost
function exhibits diseconomies of scale – the average cost curve is upward sloping.
When the production function exhibits increasing returns to scale, the long-run total
cost function exhibits economies of scale.
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5. Discuss the algebraic interpretation of the economically efficient input
combination.
Brief answer: The input combination at point e1 is economically efficient because it
minimises the firm’s cost of producing the targeted level of output.
At point e1, the slope of isoquants which is the marginal rate of technical substitution
equals to the slope of the isocost line which is equal to the input price ratio. Hence, at
MPPL
w
. Recall that MRTS =
. So, we have the
r
MPPK
MPPL w
condition for cost minimisation that
= .
MPPK r
the point of tangency: MRTS =