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Unformatted text preview: nce the is constant, Coke and Pepsi both have constant returns to variable inputs. (11.3) Founded in January 2010, Dulce & Havana (D & H) designs and manufactures high end men’s jackets right here in
Toronto. D & H manufactures jackets according to the production function:
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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. Here is number of jackets manufactured, is fixed labor, is materials, and is fixed capital. Does D & H have
increasing, constant, or decreasing returns? Provide an argument for your answer.
Answer
Since and are fixed we can substitute their values into the production function which yields; This is the output for some level of materials. If we double materials the new output is:
( ) √
√
Output with doubled input is < twice the initial output which means there are decreasing returns.
(11.4) Edison Chang has the production function
Calculate Edison Chang’s MRTS show all calculations clearly. . Suppose Edison Chang is in the long run. Answer
The long run MRTS is defined as , therefore, taking total differential of the production function and setting it equal to zero gives:
( ) ( )
(
(
(
( (
( )
) ( ) )
)
)
) (11.5) A company uses Labor (L), Capital (K) and Materials (M) as inputs to produce target output q with the production
function
.
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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. (a) For what values of will this company have constant returns to scale? Show your calculations below. Answer
Note: constant return to scale implies that if we increase inputs by a factor of
. Therefore,
(
) ( )( )( )
(
)
In order for the output to increase by a factor of ,
return to scale when
(b) For what values of
calculations below. , output must increase by a factor of
( ) must satisfy. Thus production function is constant will this company have decreasing returns with respect to materials? Show your Answer
Decreasing return to scale implies that if we increase inputs by a factor of
than . Therefore, we know that this will be true when
. , output must increase by a factor less (11.6) A company uses Labor (L) and Capital (K) as inputs to produce target output q with the production
(
)
. For what values of
will this company have increasing returns to scale? Show your
calculations below.
Answer
A production function has increasing returns to scale (
( ) ( ) if: ). That is, when the output with all inputs scaled up by a factor is greater than the output scaled up by . In lectures and
HWs, we’ve used
First, the initial output with is: Initial
(
the ) ( ) ) ( is:
( ( )
) 7
ECO 204 Chapter 11: Practice Problems & Solutions for Producer Theory – The Basics in ECO 204 (this version 2...
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