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Unformatted text preview: rns, it means that (holding k constant) doubling L doubles q. Thus and (b) What is the elasticity of output with respect to labor? Does your answer make sense give the company has constant
returns? 12
ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Answer
From part (a) . We want the elasticity of q with respect to which is Taking the ln of both sides and differentiating with respect to L yields. Therefore, if L increases by
constant returns. percent then q will also increase by percent. This makes sense given that we have (c) Suppose the company doubles labor. Without using the equation for ( ) what is the impact on total variable cost?
Average variable cost? Average cost
Answer
Total Variable Cost (TVC) is
()
If the company doubles labour, then TVC(q) must also double.
We know that () () . As the company doubles inputs (because it has constant returns) it doubles output. Thus, when the company doubles inputs, the ratio
() () () remains constant. On the other hand
() () () () With constant returns, as labout is doubled AVC(q) remains constant but AFC(q) declines with q. Thus ( ) decines. (d) Suppose the company doubles labor. Using the equation for ( ) what is the impact on total variable cost? Average
variable cost? Average cost
Answer
The cost equation is
()
With constant returns As L doubles q doubles and TVC(q) doubles, but
() ) and
() () ( ( ) (
() () )
() () ( ) which is a constant. Therefore, which declines with quantity.
13 ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (13.8) Ajax Inc. produces cranberry juice and has the short run cost function ( )
. Don Damiano Inc.
produces grape juice and has the short run cost function ( )
. If Ajax and Don Daminao merge the short run
cost function for both cranberry and grape juice is: ( )
. Are there economies of scope if Ajax and
Don Damiano merge?
Answer
To see if there economies of scope, we simply need to check if cost of cranberry and grape juices is lower than the sum
of cranberry plus grape juice.
( ) Whereas ( )
. Observe that (
)
()
( ). This
()
shows that it is cheaper to produce the juices together than separately. Therefore, there are economies of scope. 14
ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 20122013)...
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 Fall '14

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