(1) Added question (economies of scope). Let’s look at a project that has a per firm
technology of f(x)=-5+x for a unique input, x. We will assume if x is less than 5 output is
equal to zero and not consider any range of inputs below 5.
(A) What type of economies of scale (remember there are three possible does this
technology have for its entire range? Why? What is true of its average per unit cost?
(Assume each unit of input x has cost one for this.) Can you graph that? What is the
relationship between average costs and economies of scale?
(B) Let’s look at a function that has different returns of scale defined by the average per
unit of cost of AC(y)=y-14+51/y. [Hint this is a parabola with a definite minimum
value.] Plot this. Where does this function have increasing, constant or decreasing
returns? Note that returns to scale can imply to changes in inputs that are less than
doubling.
(C) Suppose there are two firms with the same technology. Let’s assume that we require
any amount y to be produced by two firms who produce identical quantities y/2, let’s
call the resulting average costs to both firms combined as AC2(y)? It turns out that
AC2(y) is the cheapest way to organize production between these two firms. Why?
(D) Plot AC(y) and AC2(y) on the same graph. Graph the minimum of the two functions.
The region of the graph where AC(y) corresponds to the minimum is called the
subadditive region. What do you think is the economic significance of this region?
What is the relationship between subadditivity and returns to scale in this graph?
In general, can you think of an economic question where subadditivity might be a more
useful concept than economies of scale?
(E) In models where firms produce multiple goods, the number of markets in which average
costs are minimized by having positive production from the same firm is called
economies of scope. Let’s say there are two goods, y1 and y2. Can you give an average
cost function with positive economies of scope? How about one with negative
economies of scope?
(2) Solve questions 1-4 from Chapter 19.
(3) Extra Credit: Attach photocopied notecards of study questions for Chapter 19.
Arrange as many cards on a given sheet of paper before photocopying as you feel
comfortable.
...
(1) Added question (economies of scope). Let’s look a.docx
1. (1) Added question (economies of scope). Let’s look at a
project that has a per firm
technology of f(x)=-5+x for a unique input, x. We will assume
if x is less than 5 output is
equal to zero and not consider any range of inputs below 5.
(A) What type of economies of scale (remember there are three
possible does this
technology have for its entire range? Why? What is true of its
average per unit cost?
(Assume each unit of input x has cost one for this.) Can you
graph that? What is the
relationship between average costs and economies of scale?
(B) Let’s look at a function that has different returns of scale
defined by the average per
unit of cost of AC(y)=y-14+51/y. [Hint this is a parabola with
a definite minimum
value.] Plot this. Where does this function have increasing,
constant or decreasing
returns? Note that returns to scale can imply to changes in
inputs that are less than
doubling.
(C) Suppose there are two firms with the same technology.
Let’s assume that we require
any amount y to be produced by two firms who produce
identical quantities y/2, let’s
call the resulting average costs to both firms combined as
2. AC2(y)? It turns out that
AC2(y) is the cheapest way to organize production between
these two firms. Why?
(D) Plot AC(y) and AC2(y) on the same graph. Graph the
minimum of the two functions.
The region of the graph where AC(y) corresponds to the
minimum is called the
subadditive region. What do you think is the economic
significance of this region?
What is the relationship between subadditivity and returns to
scale in this graph?
In general, can you think of an economic question where
subadditivity might be a more
useful concept than economies of scale?
(E) In models where firms produce multiple goods, the number
of markets in which average
costs are minimized by having positive production from the
same firm is called
economies of scope. Let’s say there are two goods, y1 and y2.
Can you give an average
cost function with positive economies of scope? How about
one with negative
economies of scope?
(2) Solve questions 1-4 from Chapter 19.
(3) Extra Credit: Attach photocopied notecards of study
questions for Chapter 19.
Arrange as many cards on a given sheet of paper before
photocopying as you feel
comfortable.
![(1) Added question (economies of scope). Let’s look at a
project that has a per firm
technology of f(x)=-5+x for a unique input, x. We will assume
if x is less than 5 output is
equal to zero and not consider any range of inputs below 5.
(A) What type of economies of scale (remember there are three
possible does this
technology have for its entire range? Why? What is true of its
average per unit cost?
(Assume each unit of input x has cost one for this.) Can you
graph that? What is the
relationship between average costs and economies of scale?
(B) Let’s look at a function that has different returns of scale
defined by the average per
unit of cost of AC(y)=y-14+51/y. [Hint this is a parabola with
a definite minimum
value.] Plot this. Where does this function have increasing,
constant or decreasing
returns? Note that returns to scale can imply to changes in
inputs that are less than
doubling.
(C) Suppose there are two firms with the same technology.
Let’s assume that we require
any amount y to be produced by two firms who produce
identical quantities y/2, let’s
call the resulting average costs to both firms combined as](https://image.slidesharecdn.com/1addedquestioneconomiesofscope-221031050549-e0ff8df4/85/1-Added-question-economies-of-scope-Let-s-look-a-docx-1-320.jpg)
