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Unformatted text preview: ur answer to part (a) in Figure 1 below. Now suppose
labor in Figure 1 below: decreases: graph the resulting demand curve for (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. (b) Characterize ABC’s returns to scale. Given your answer, sketch a graph of average cost versus output below. Please
show all calculations below.
(c) Derive ABC’s (longrun) cost function. Please show all calculations below and state any assumptions.
(11.9) A company uses labor and capital as complements to produce output according to the production function:
(
Here, is a parameter for technological progress and ) is a parameter. Assume .
2 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) What is this company’s “returns to scale”?
(b) Solve for the optimal (long run) labor and capital demands. Show all calculations.
(c) Derive the (long run) cost function.
(d) Plot the
curve.
Hint #1: there are 3 different curves corresponding to increasing, constant and decreasing returns to scale.
Hint #2: for increasing and decreasing returns to scale, look at
for
and
.
Hint #3: If you’re having issues, look at
for
and respectively.
Hint #4: remember that with is constant and with increases with output and with declines with output.
(11.10) Three competitive firms A, B and C hire workers at
functions are: and lease machines at . Their production Firm A Firm B
( ) Firm C Assume . Assume all firms have target output . (a) Characterize each firm’s returns to scale. Show all calculations.
(b) between firms A and C which one exhibits dimishing marginal return.
(11.11) Ajax Cola, a soft drinks manufacturer, uses a technology that combines equal amounts of sweetener, labor ( ),
capital ( ), and materials ( ) as complementary inputs to produce soft drinks ( ). Currently, Ajax Cola uses sugar ( ) as
a sweetener.
Ajax purchases/hires/leases all inputs as a price taker. Denote the price of sugar by
the wage rate by
rental rate by , and the price of materials by . In this question, assume all inputs are variable. , the capital (a) Write down Ajax Cola’s production function and characterize its returns to scale. Show all calculations below.
(b) Calculate the optimal inputs required to produc...
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This document was uploaded on 01/19/2014.
 Fall '14

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