Unformatted text preview: e
variable cost? Average cost
(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? 2
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. Solutions
(13.1) True, False: Short run cost of production to produce a target output is smaller than its long run cost of
production. Explain your answer and give a graphical analysis to support your answer. You can assume CobbDouglas
production function.
Answer
The statement is false. Let’s assume production function is of the form (
) , where K is for capital and L for labour.
Since capital is fixed in the short run we can only choose labor to produce the target quantity of output, which this does
not mean that the optimal condition is satisfied (i.e. cost is minimized). Please see the diagram on page 3 of the chapter.
(13.2) State the optimal labor rule and explain under what condition it hold.
Answer
Marginal Benefit of an additional unit of labor = Marginal Cost of an additional unit of labor
Please refer to page 11 of the chapter for the derivation.
(13.3) Given the following production function, state under what conditions it is increase, decreasing and constant
returns. Where is quantity Answer
Let’s since is fixed capital, denote labour, material input 1, and material input 2, respectively. is fixed. Therefore,
( If we increase variable inputs by
( ) amount we get
) ( )( )( ) ( ) Therefore
The short run production function exhibits { (
(
( )
)
) Note: how this is different from increasing, decreasing and constant return to scale.
(13.4) Consider a c...
View
Full
Document
This document was uploaded on 01/19/2014.
 Fall '14

Click to edit the document details