Chillman Motors, Inc., believes it faces the following segmented demand function:
P = 150-0.5Q when 0 (is less than or equal to) Q (is less than or equal to) 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+0.5Q^2
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+0.5Q^2
e) If Chillman's total cost function changes to either: TC3=500+15Q+1.0Q^2 or TC4-500+5Q+0.25Q^2
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?