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2.4 Q7 In the theory of the firm, economist consider the total cost to be a function of the output level Q: C=f(Q). (a) According to the definiton of a function, should each cost figure be associated with a unique level of output? (b) should each leyel of output determine a unique cost figure?

2.4 Q7 In the theory of the firm, economist consider the total cost to be a function of the output level Q: C=f(Q). (a) According to the definiton of a function, should each cost figure be associated with a unique level of output? (b) should each leyel of output determine a unique cost figure?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2.4

Q7

In the theory of the firm, economist consider the total cost to be a function of the output level Q: C=f(Q).

(a) According to the definiton of a function, should each cost figure be associated with a unique level of output?

(b) should each leyel of output determine a unique cost figure?

Ex (1) & (2)- Support materials The Nature of Mathematical Economics Mathematical cconomics is not a distinct branch of economics in the sense that public fi- nance or international trade is. Rather, it is an approach to economic analysis, in which the conomist makes use of mathematical symbols in the statement of the problem and also draws upon known mathematical theorcms to aid in reasoning. As far as the specific sub- ject matter of analysis goes, it can be miero- or macroeconomic theory, public finance, urban economies, or what not. Using the term mathematical economics in the broacdest possible sense, one may very well say that every elementary textbook of economics today exemplifies mathematical cco- nomics insofar as geometrical methods are frequently utilized to derive theoretical results. More commonly, however, mathematical economics is reserved to describe cases employ- ing mathematical techniques beyond simple gcometry, such as matrix algebra, differential and integral calculus, differential equations, difference equations, ete. It is the purpose of this book to introduce the reader to the most fundamental aspects of these mathematical methods- those encountered caily in the current economic literature. EXERCISE 2.4 4 1. Given S1 = {3,6,9}, S2 = {0, b}, and S3 = {m, n}, find the Cartesian products: (0) S1 x S2 2. From the information in Prob. 1, find the Cartesian product S1 x S2 x S3. 3. In general, is it true that S1 × S2 = S2 x S1? Under what conditions will these two Cartesian products be equal? 4. Does any of the following, drawn in a rectangular coordinate plane, represent a (b) S2 x S3 (c) S3 x S1 function? (a) A circle (b) A triangle 5. If the domain of the function y = 5+ 3x is the set (x | 1 < x < 9}, find the range of the function and express it as a set. (c) A rectangle (d) A downward-sloping straight line 6. For the function y = -x², if the domain is the set of all nonnegative real numbers, what will its range be? 7. In the theory of the firm, economists consider the total cost C to be a function of the output level Q: C = f(Q). (a) According to the definition of a function, should each cost figure be associated with a unique level of output? (b) Should each level of output determine a unique cost figure? 8. If an output level Qi can be produced at a cost of C1, then it must also be possible (by being less efficient) to produce Q, at a cost of C, + $1, or Ci + $2, and so on. Thus it would seem that output Q does not uniquely determine total cost C. If so, to write C = f(Q) woutd violate the definition of a function. How, in spite of the this reasoning, would you justify the use of the function C = i(Q)? EXERCISE 3.2 1 Chen the market mode
Transcribed Image Text:Ex (1) & (2)- Support materials The Nature of Mathematical Economics Mathematical cconomics is not a distinct branch of economics in the sense that public fi- nance or international trade is. Rather, it is an approach to economic analysis, in which the conomist makes use of mathematical symbols in the statement of the problem and also draws upon known mathematical theorcms to aid in reasoning. As far as the specific sub- ject matter of analysis goes, it can be miero- or macroeconomic theory, public finance, urban economies, or what not. Using the term mathematical economics in the broacdest possible sense, one may very well say that every elementary textbook of economics today exemplifies mathematical cco- nomics insofar as geometrical methods are frequently utilized to derive theoretical results. More commonly, however, mathematical economics is reserved to describe cases employ- ing mathematical techniques beyond simple gcometry, such as matrix algebra, differential and integral calculus, differential equations, difference equations, ete. It is the purpose of this book to introduce the reader to the most fundamental aspects of these mathematical methods- those encountered caily in the current economic literature. EXERCISE 2.4 4 1. Given S1 = {3,6,9}, S2 = {0, b}, and S3 = {m, n}, find the Cartesian products: (0) S1 x S2 2. From the information in Prob. 1, find the Cartesian product S1 x S2 x S3. 3. In general, is it true that S1 × S2 = S2 x S1? Under what conditions will these two Cartesian products be equal? 4. Does any of the following, drawn in a rectangular coordinate plane, represent a (b) S2 x S3 (c) S3 x S1 function? (a) A circle (b) A triangle 5. If the domain of the function y = 5+ 3x is the set (x | 1 < x < 9}, find the range of the function and express it as a set. (c) A rectangle (d) A downward-sloping straight line 6. For the function y = -x², if the domain is the set of all nonnegative real numbers, what will its range be? 7. In the theory of the firm, economists consider the total cost C to be a function of the output level Q: C = f(Q). (a) According to the definition of a function, should each cost figure be associated with a unique level of output? (b) Should each level of output determine a unique cost figure? 8. If an output level Qi can be produced at a cost of C1, then it must also be possible (by being less efficient) to produce Q, at a cost of C, + $1, or Ci + $2, and so on. Thus it would seem that output Q does not uniquely determine total cost C. If so, to write C = f(Q) woutd violate the definition of a function. How, in spite of the this reasoning, would you justify the use of the function C = i(Q)? EXERCISE 3.2 1 Chen the market mode
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