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Unformatted text preview: ) A 1% increase in TFC raises the average rational smelter’s loss by 2.92% or from a loss of ($14,373) to a loss of ($14,793). 54
ECO 204 Chapter 12: Practice Problems & Solutions for The Long 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. (12.13) Ajax Bus Company (ABC) operates a bus service between Robarts library and the Rotman School of
Management. Each ABC bus (capital) carries 100 passengers and requires a driver and a conductor (labor).
Let
number of buses/day,
number of workers (labor) per day, and
number of passengers/day. Denote the
price of leasing (or owning) buses per day by
and daily wages by (assume that drivers and conductors have the
same daily wage). In this question, all inputs are variable.
( ) (a) If ABC wishes to carry passengers per day, what is the optimal (cost minimizing) number of buses and labor per
day? That is, solve the problem:
( ) Answer
This problem cannot be solved by the Lagrangian method since the production function is not differentiable everywhere.
Instead, note that at the optimal choice of inputs it must be that:
(
Notice
And: ) is solved in chapter 11 practice problems (11.8) part (a). This implies:
( ) And:
( ) That is: This makes sense: 100 passengers required 1 bus ( ) and two workers ( )
55 ECO 204 Chapter 12: Practice Problems & Solutions for The Long 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. (b) Derive ABC’s (longrun) cost function. Please show all calculations below and state any assumptions.
Answer
From above: The cost function is:
()
() ()
(c) This question should be answered independently of all other questions (i.e. the numbers given here for
and
are for this question only). Suppose
and can be either $20 with probability ¾ or $40 with probability
¼. Calculate ABC’s expected cost of carrying passengers. Please show all calculations below.
Answer
From above:
()
Here with certainty; wages are uncertain and are expected to be: Thus, the expected cost will be:
[ ( )] [ ( )] [ ( )] 56
ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run...
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