CLASS ASSIGNMENT
What is the relation between the Constant Elasticity of Substitution (CES)
production function, the Cobb-Douglas production function, and the Leontief
production function?
The Cobb-Douglas production function is a special case of CES where sigma=1
The Leontief production function is a special case of CES where sigma=0
Economies of scale can explain why the unit cost of a product has fallen over the
past decade. What exactly is that explanation – how does it work?
That explanation would work if the scale of production of that commodity had
significantly increased over the past decade. With economies of scale and the
larger scale of production, the unit cost of the product would be expected to fall.
If a production function exhibits increasing returns to scale and the scale of output
is doubled, what happens to the average cost per unit produced?
AC per unit declines as output rises
If a production function exhibits constant returns to scale and the scale of output
is doubled, what happens to the average cost per unit produced?
AC per unit stays constant as output rises
What does it mean if a production function exhibits diseconomies of scale?
It implies that, as the scale of production increases , the average cost per unit
produced rises , production becomes more costly.
Give an example of an industry marked by strong economies of scale.
Utility industries
What is learning by doing?
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Refers to the notion that productivity increases as a result of the cumulative
experience and knowledge gained from producing a product since it was first
introduced.
How does it differ from economies of scale?
Learning by doing, the current cost of production depends not just on current
output , but also on cumulative output since production first began.
Give me an example of an industry where learning by doing has had an important
impact.
Learning by doing may be especially important for brand new technologies
Technological change can be represented by a change in the set of isoquants –
what change?
There is downward shift in the isoquants –perhaps just a parallel shift, perhaps
not. You can obtain the same output as before with less inputs.
If input prices stay the same and there is neutral technological change, how does
this affect the factor intensity of the firm’s cost-minimizing input choices?
neutral technological change raises MPL and MPk equally along every ray through
the origin, so the MRTS stays the same.
If input prices stay the same and there is non-neutral technological change, how
does this affect the factor intensity of the firm’s cost-minimizing input choices?
Non-neutral technical change raises MPL and MPK differentially along every ray
through the origin. Therefore, the MRTS (isoquant slope) changes along any given
ray through the origin.
If input prices stay the same and there is non-neutral, capital -saving technological
change, how does this affect the factor intensity of the firm’s cost-minimizing
input choices?
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Raises MPL more than it raises MPK, if input prices stay constant and same output
is produce, outcome is to use less capital and more labor. But output could
increase as a result of technical change.
If input prices stay the same and there is non-neutral, labor -saving technological
change, how does this affect the factor intensity of the firm’s cost-minimizing
input choices?
Raises MPL more than it raises MPK, if input prices stay constant and same output
is produce, outcome is to use less labor and more capital, But output could
increase as a result of technical change.
Give me a real-world example of non-neutral technical change and tell me
whether it was capital- or labor-saving.
Replacing horse dawn ploughs with tractors on farms
Learning by doing and technical change are both factors that can explain why the
unit cost (average cost) of manufacturing a product might change over time.
Might it be difficult to tell them apart?
They both play out over time –the accumulation of experience in producing the
commodity over time, and technical change occurring over time. Both may occur
together if it is a new technology (e.g. rooftop solar),the development of the
technology is an innovation (a technical change) and also, precisely because it is
new, there is learning by doing in manufacturing it.
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PROFIT MAXIMIZATION, UNCONDITIONAL INPUT DEMAND AND OUTPUT SUPPLY
Describe the firm’s profit-maximization decision: what variables are being selected
and what is the objective function? Now give an alternative answer to the
question of what variables are being selected?
Choose input x1,…,Xn, TO MAXIMIZE PF(X1,…,XN)-sum of wixi
Choose output y, maximize py-C(w1,…,Wn,y)
What variables does the firm take as given in its profit maximization decision?
Output price and input prices: p, w1, w2,...,wN
What is the relationship between cost minimization and profit maximization?
Cost minimization is part of profit maximization, profit maximization is more than
cost minimization.
Can you have profit maximization without cost minimization?
No
Can you have cost minimization without profit maximization?
Yes
What is meant by the value of the marginal product of labor?
It VMP measures the additional revenue earned from the additional output
produced by using an extra unit of labor input.
What is the condition for choosing the profit maximizing quantity of labor?
Expand the labor input up to the point where the VMPL = wage rate
What is the condition for choosing the profit maximizing level of output?
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Expand output up to the point where the marginal cost equals output price
What does the unconditional input demand function represent? What variables
appear on the right-hand side of the unconditional input demand function?
It represents the profit-maximizing quantity of an input to select, as a function of
the price of output and the prices of the inputs.
How does this differ from the variables that appear on the right-hand side of the
conditional input demand functions?
The conditional input demand show the cost-minimizing quantity of an input to
select as a function of the target output to be produced and the prices of all the
inputs.
What does the output supply function represent? What variables appear on the
right-hand side of the output supply function?
It represents the profit-maximizing quantity of output to supply, as a function of
the price of output and the prices of the inputs.
In the diagram here, is the price of paper is $276/ton, what is the profit
maximizing quantity of paper to produce?
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What is the profit maximizing output if, at the output Q* where p = MC(Q*), it
turns out that AVC(Q*) > p.
Rather than produce Q*, the firm should produce Q = 0
Suppose a firm’s marginal cost is given by: MC(y) = 20 + 3y. What is the formula for
the firm’s output supply curve?
P=MC
P=MC=20+3y
What qualification applies to the firm’s supply rule?
Supply rule is p=MC as long as p>AVC
Suppose pollution control regulations raise the firm’s fixed cost but not its variable
costs; how does that affect its output supply curve?
The firm’s supply curve is the portion of its marginal cost curve that lies above its
average variable cost curve.
Suppose pollution control regulations raise the firm’s variable costs but not its
fixed cost; how does that affect its output supply curve?
This affect both Solvaks average variable cost and its marginal cost.
How are a firm’s unconditional demand function for labor and its conditional
demand function for labor connected?
Take the conditional input demand function, and let the level of output in that
demand be varied according to the output supply function. That gives the
unconditional input demand function.
Which demand function will exhibit a larger own price elasticity of demand for an
input – the conditional demand function for the input or the unconditional
demand for that input? What part of the demand response to an input price
increase is different as between the two types of input demand function?
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What is measured by the area shown in the diagram under the firm’s value of
marginal product curve up to the input quantity x’?
If input usage is x’, the gross revenue
earned from that level of input usage is
given by the shaded area.
What is measured by the shaded area
in the following diagram?
measures the net revenue earned by the firm
The price paid by the firm for an input falls
from w’ to w”. What is measured by the
shaded area in the following diagram?
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