# An introduction to mathematics for economics by Akihito Asano

By Akihito Asano

''An advent to arithmetic for Economics introduces quantitative tips on how to scholars of economics and finance in a succinct and obtainable kind. The introductory nature of this textbook capacity a historical past in economics isn't really crucial, because it goals to aid scholars delight in that studying arithmetic is suitable to their total realizing of the topic. financial and monetary purposes are defined inRead more...

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What is y 3 in terms of q? This can be solved by directly applying the deﬁnition of the power: y3 = q4 3 = q 4 · q 4 · q 4 = q 4+4+4 = q 4×3 = q 12 . 2 n = q mn . 3) 1 2 Up to this point, m and n were implicitly treated as integers and hence numbers were raised to some integers. But numbers need not be raised to integers only and the power rules can be applied for non-integers as well. To delve into this issue, let us look at the following statement: q n = y. 3) that: Non-integer powers, particularly q n = y n ×n = y n 1 1 and hence: 1 q = yn ≡ n , √ n y.

Recall the real line we discussed previously. 2. The plane made by these two lines (just imagine placing a piece of paper on the two lines) is called the coordinate plane. The horizontal line is called the horizontal axis and the other one is called the vertical axis. The intersection of the two axes is called the origin. Let us think of the case where x is taken on the horizontal axis and y is taken on the vertical axis. When you draw the coordinate plane, it is important that you write down what you take on the two axes.

The above relationship can be represented as d = f (N, T ). N and T are called arguments of this function. More speciﬁcally, we say that N is the ﬁrst argument and T is the second argument. To conclude this subsection, I note that a function can have more than two arguments. In general, we can write y = f (x1 , x2 , . . , xn ). It means that y is a function of n arguments, x1 , x2 , . . , xn . We will discuss the multivariate function in the context of a consumer’s utility maximisation problem in Chapter 6.