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Advanced Microeconomics

What is the production function?

f(x) = {y e R: y is the max. ouput associated with (y,-x) e Y}

Advanced Microeconomics

What is the implicit assumption when we have monotonicity of a production function?

We implicilty assume free disposal of inputs is possible.

Advanced Microeconomics

What does convex technology mean?

Convexity means: If x

and x‘‚ are in V(y), then

tx + (1-t)x' is in V(y)

for all 0≤ t ≤ 1.

V(y) is a convex set.

Advanced Microeconomics

What is the technical rate of substitution?

In the two output case it is equivalent to the slope of the isoquant:

how one has to adjust x2 to keep output constant when x1 changes by a small amount.

Advanced Microeconomics

When do we have constant returns to scale?

We have constant returns to scale if any of the following are satisfied:

1. y e Y implies ty e Y, for all t ≥ 0

2. x e V(y) implies tx e V(y) for all t ≥ 0

3. f(tx)=tf(x) for all t ≥ 0; i.e. the production function is homogeneous of degree 1.

Advanced Microeconomics

When do we have increasing returns to scale?

We have increasing returns to scale if f(tx) > tf(x) for all t > 1

Advanced Microeconomics

When do we have decreasing returns to scale?

We have decreasing returns to scale if f(tx) < tf(x) for all t > 1

Advanced Microeconomics

How is the economic profit defined?

Revenue of a firm minus its costs

Advanced Microeconomics

What behavioral assumption is used for analyzing firms?

We use the assumption of profit maximization.

Advanced Microeconomics

What does the factor demand function present?

The factor demand function gives us the optimal choice of inputs as a function of the prices. It is denoted by x(**p,w**)

Advanced Microeconomics

What is the supply function of the firm?

y(**p**,w) = f(x(p,**w**)

Advanced Microeconomics

What do we assume about the factor demand and supply function?

We assume they are well defined and nicely behaved.

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