This preview shows page 1. Sign up to view the full content.
Unformatted text preview: output is: (
(d) Plot the ) ( ) ( )( ) curve. Hint #1: there are 3 different curves corresponding to increasing, constant and decreasing returns to scale.
Hint #2: for increasing and decreasing returns to scale, look at
for
and
.
Hint #3: If you’re having issues, look at
for
and respectively.
Hint #4: remember that with is constant and with increases with output and with declines with output.
Answer:
From the cost function:
( )
( (
)( ) (
( ) )(
)( )
) Examine each case separately:
Case 1:
or constant RTS.
We know the AC must be constant. In fact, setting
( :
)( ) This is intuitive  doubling inputs (always) doubles cost and with constant returns to scale doubles output. Thus the ratio
remains constant. This is depicted below. 14
ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Case 2:
or decreasing RTS.
We know the AC must rise with output. The AC is:
(
Observe that if then ) To see where AC is zero and positive:
( And observe: when )( )( ) then:
( ) This is depicted below: 15
ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Case 3:
or increasing RTS.
We know the AC must decrease with output. The AC is:
(
Because the term ( ) . Thus, when )( ) then When then: Hence, AC is decreasing in q (as it should be with increasing RTS) and is: (11.10) Three competitive firms A, B and C hire workers at
functions are: and lease machines at . Their production 16
ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Firm A Firm B
( ) Firm C Assume . Assume all firms have target output . (a) Characterize each firm’s returns to scale. Show all calculations.
Answer:
We need to check if the output with doubled inputs is more than, equal to, or less than, twice the output with initial
inputs.
Start with firm A. Doubling all inputs produces:
( ) ( ) ( ) ( ) Firm A has constant returns to scale,
Next, firm B. Doubling all inputs produces:
( ) ( ) ( ) ( ) Firm B also has constant returns to scale,
Next, firm C. Doubling all inputs produces:
( ) ( ) Firm C also has constant returns to scale,
(b) between firms A and C which one exhibits dimishing marginal return.
Answer
Firm A:
To find which firm exhibit diminishing marginal return we need to calculate the marginal product of each input factor,
that is:
( ) ( ) Graphing this, 17
ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The
is increasing but in a decreasing rate...
View
Full
Document
This document was uploaded on 01/19/2014.
 Fall '14

Click to edit the document details