Unformatted text preview: 0122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. We need to see when the output with twice the inputs is greater than double the initial output. Double the initial output
is:
Double Initial
(
New output ) Double initial output when:
( ) ( ) ( ) Which can only happen if γ < 0.
If you’re having problems seeing this, you can use that:
(
( )
( Thus: ( ) ) (
) ) ( has increasing returns to scale when ) . (11.7) ETorre Enterprises used labor (L) and capital (K) to produce its target output q according to the production
function
where
and
. ETorre procures labor and capital in competitive markets.
Currently,
and
.
(a) If ETorre is in the long run, how much labor and capital does it use? Show your calculations below.
Answer
ETorre has a perfect substitute’s production function. Optimal labor and capital depends on whether the isocost is
steeper, tangent, or flatter than the isoquant.
The isocost has slope
The isoquant has slope . Given the isocost is steeper than the isoquant, ETorre will use zero labor. Thus, 8
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. Incidentally, the y and x intercepts of the isoquant are 10 and 40 respectively.
(b) Plot your answer to part (a) in Figure 1 below. Now suppose PL decreases: graph the resulting demand curve for labor
in Figure 1 below:
Answer (11.8) 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) In order to model ABC’s technology, what is in the following production function:
( Use the chosen value of ) for the remainder of the exam. Please give a brief explanation for your answer below.
9 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. Answer
We know that 1 bus and 2 workers are needed to carry 100 passengers. Therefore:
( ) ( ) (b) Characterize ABC’s returns to scale. Given your answer, sketch a graph of average cost versus output below. Please
show all calculations below.
Answer
Complements production functions always have constant returns to scale (not always true but the most likely outcomesee for example question 11.6 and 11.9 where CRTS is violated). Let’s check this. The output with some arbitrary level of
capital and labor is:
( ) Doubling labor and capital yields the out...
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