Case for Instructiecollege 2, Economics 1.2, Bedrijfskunde. Theory of the firm.
Part 1. Theory of the firm
In this case we apply the basics of the theory of the firm. We look at a firm that produces
an amount of output Q with input factors labour L (in hours) and capital K. It has the
following production function:
Q L0.5 K 0.5
The price of labour is equal to w = 12, and the rental price of capital is r = 3. These input
prices cannot be influenced by the firm.
A. Determine the marginal productivity of labour and capital for this production
technology.
B. Is the marginal productivity of labour increasing, constant, or decreasing in
labour?
C. What is an isoquant?
D. Determine the marginal rate of technical substitution (MRTS) for this production
technology, if we would have capital at the vertical axis and labour at the
horizontal axis.
E. What conclusion can we draw from the MRTS that you found for the shape of the
isoquant?
F. Determine the isocosts line for this firm.
G. The isocosts for the firm somehow resemble the budgetline for a consumer. What
is a similarity between the isocosts and the budgetline, and what is an important
difference?
H. If K = 36 and L = 8, would the firm want to increase or decrease its capital-labour
ratio or would it want to keep it the same, given the production technology and
the given values of the prices of the input factors?
I. If the firm wants to produce Q =18 units of output, how many units of capital and
labour would it need to employ to minimize costs?
J. Suppose we are in a short run situation and the amount of capital is fixed at K =
36. Determine the firm’s short run cost function c(Q). What are the variable costs,
and what are the fixed costs?
K. Determine the firm’s average costs and the firm’s marginal costs.
L. Discuss the importance of the marginal costs and average costs for the decision of
the manager of the firm.
M. In the long run capital K is variable as well. Determine the firm’s long run cost
function. What are the firm’s fixed costs?
N. Are the returns to scale constant, increasing, or decreasing for this firm?
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Part 1. Theory of the firm
In this case we apply the basics of the theory of the firm. We look at a firm that produces
an amount of output Q with input factors labour L (in hours) and capital K. It has the
following production function:
Q L0.5 K 0.5
The price of labour is equal to w = 12, and the rental price of capital is r = 3. These input
prices cannot be influenced by the firm.
A. Determine the marginal productivity of labour and capital for this production
technology.
B. Is the marginal productivity of labour increasing, constant, or decreasing in
labour?
C. What is an isoquant?
D. Determine the marginal rate of technical substitution (MRTS) for this production
technology, if we would have capital at the vertical axis and labour at the
horizontal axis.
E. What conclusion can we draw from the MRTS that you found for the shape of the
isoquant?
F. Determine the isocosts line for this firm.
G. The isocosts for the firm somehow resemble the budgetline for a consumer. What
is a similarity between the isocosts and the budgetline, and what is an important
difference?
H. If K = 36 and L = 8, would the firm want to increase or decrease its capital-labour
ratio or would it want to keep it the same, given the production technology and
the given values of the prices of the input factors?
I. If the firm wants to produce Q =18 units of output, how many units of capital and
labour would it need to employ to minimize costs?
J. Suppose we are in a short run situation and the amount of capital is fixed at K =
36. Determine the firm’s short run cost function c(Q). What are the variable costs,
and what are the fixed costs?
K. Determine the firm’s average costs and the firm’s marginal costs.
L. Discuss the importance of the marginal costs and average costs for the decision of
the manager of the firm.
M. In the long run capital K is variable as well. Determine the firm’s long run cost
function. What are the firm’s fixed costs?
N. Are the returns to scale constant, increasing, or decreasing for this firm?
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