Problem Set B 1. The demand function for a good is given by the equation P = a – bQ while the total cost function is TC = dQ² + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit. (b) Derive an expression for the value of Q for which profit is maximised. %3D

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Problem Set B
1. The demand function for a good is given by the equation P = a – bQ while the total
cost function is TC = dQ² + eQ+f, where a, b, d, e and f are positive constants.
(a) Derive the equation for profit.
(b) Derive an expression for the value of Q for which profit is maximised.
(2) For the f(x) = -x3 + 3x + 6 determine the coordinates of the turning point(s) and
any point(s) of inflection, if they exist.
Transcribed Image Text:Problem Set B 1. The demand function for a good is given by the equation P = a – bQ while the total cost function is TC = dQ² + eQ+f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit. (b) Derive an expression for the value of Q for which profit is maximised. (2) For the f(x) = -x3 + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of inflection, if they exist.
(3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge
gained in Unit 1 and 2, show that:
1
+
x +
1
h
4
(a) Lim
X-0
(b) Ļim
h-0 V5h + 4 - 2
= -2
%3D
X
1
= 3.
(c) Lim
t-1 t-1
Transcribed Image Text:(3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in Unit 1 and 2, show that: 1 + x + 1 h 4 (a) Lim X-0 (b) Ļim h-0 V5h + 4 - 2 = -2 %3D X 1 = 3. (c) Lim t-1 t-1
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