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price-output solution

This question is about chapter 11 , " price & output decision" in economics for managers by Harris

Motors co., believes it faces the following segmented demand function:

P = 150 - 0.5Q when 0 ≤ Q ≤ 50
P = 200 - 1.5Q for Q > 50

a) Indicate both verbally and graphically why such a segmented demand function is likely to exist. What type of industry structure is indicated by this relationship?
b) Calculate the marginal revenue functions facing Chillman. Add these to your graph from Part (a)
c) Chillman's total cost function is

TC1 = 500 + 15Q + .5Q2

Calculate the marginal cost function. What is Chillman's profit-maximizing price and output combination?
d) What is Chillman's profit-maximizing price-output combination if total costs increase to
TC2 = 500 + 45Q + 0 .5Q2

e) If Chillman's total cost function changes to either

TC3 = 500 + 15Q + 1.0Q2

Or

TC4 = 500 + 5Q + .25Q2

What price-output solution do you expect to prevail? Would your answer change if you knew that all firms in the industry witnessed similar changes in their cost functions?

Solution Preview

See the attached file. The text here may not print the graphs and tables properly. Thanks
Motors co., believes it faces the following segmented demand function:

P   = 150 - 0.5Q when 0 ≤ Q  ≤  50
P   = 200 - 1.5Q       for Q  > 50

a) Indicate both verbally and graphically why such a segmented demand function is likely to exist. What type of industry structure is indicated by this relationship?
P Q
150 0
145 10
140 20
135 30
130 40
125 50
125 50
110 60
95 70
80 80
65 90
50 100
35 110
20 120
5 130
0 133

"The industry structure is oligopoly or monopolistically competitive market. And the demand curve is kinked demand curve. This type of demand structure exist as firms will not raise their prices as even a small price increase would result in loss of many customers. On the other hand, firm may not also decrease their price as the price elasticity for decrease in price is low and the firm will gain only a few customers ...

Solution Summary

A price-output solution is presented.

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