2.4Q7In 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 materialsThe Nature ofMathematical EconomicsMathematical 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 theconomist makes use of mathematical symbols in the statement of the problem and alsodraws 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 verywell 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, differentialand integral calculus, differential equations, difference equations, ete. It is the purpose ofthis book to introduce the reader to the most fundamental aspects of these mathematicalmethods- those encountered caily in the current economic literature.EXERCISE 2.441. Given S1 = {3,6,9}, S2 = {0, b}, and S3 = {m, n}, find the Cartesian products:(0) S1 x S22. 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 twoCartesian products be equal?4. Does any of the following, drawn in a rectangular coordinate plane, represent a(b) S2 x S3(c) S3 x S1function?(a) A circle(b) A triangle5. If the domain of the function y = 5+ 3x is the set (x | 1 < x < 9}, find the range of thefunction and express it as a set.(c) A rectangle(d) A downward-sloping straight line6. For the function y = -x², if the domain is the set of all nonnegative real numbers, whatwill its range be?7. In the theory of the firm, economists consider the total cost C to be a function of theoutput level Q: C = f(Q).(a) According to the definition of a function, should each cost figure be associated witha 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 (bybeing less efficient) to produce Q, at a cost of C, + $1, or Ci + $2, and so on. Thus itwould seem that output Q does not uniquely determine total cost C. If so, to writeC = 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 3.21 Chen the market mode

According to the mathematical definition of the function, it is a relation which associates each…

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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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