By Akihito Asano

''An creation to arithmetic for Economics introduces quantitative the right way to scholars of economics and finance in a succinct and available kind. The introductory nature of this textbook capacity a historical past in economics isn't crucial, because it goals to aid scholars delight in that studying arithmetic is appropriate to their total figuring out of the topic. fiscal and monetary purposes are defined inRead more...

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**Extra info for An introduction to mathematics for economics**

**Example text**

We will again put off the discussion as to why the graph shapes like that until Chapter 5. 8 The graph of p(q) = 4 . q Denoting f (x) = y, note that the above function can be rearranged as xy = a. It means the product of the two variables x and y is always constant at a. Note also that neither x nor y can be zero (if either is zero, the product of the two can never be a positive number). This means that the function never cuts the axes. Instead, the curve approaches the axes asymptotically. That is, the curve will come closer and closer to the horizontal axis as x becomes larger and larger; and will become closer and closer to the vertical axis as y becomes larger and larger.

Question Explain why the equilibrium price cannot stay the same if there is the change in the demand as explained above. Obtain the new equilibrium price. Solution If the price of apples stayed the same as the original equilibrium price, which is 4, there would be an excess demand (or a shortage) of apples. This leads apple buyers to bid the price up. Apple sellers who realise the shortage will also raise the price. e. until it reaches the new equilibrium price. The new system of equations is p =q +2 p = 14 − q 2 Substituting the second equation into the ﬁrst one yields: 14 − q 2 = q + 2.

9 Case-deﬁned function. Question C g(f (x)). Solution Take two functions: f (x) = 2x 2 and g(x) = 3x 2 . Obtain f (g(x)) and The order you substitute functions matters. f (g(x)) = 2(3x 2 )2 = 2 · 9x 4 = 18x 4 . g(f (x)) = 3(2x 2 )2 = 3 · 4x 4 = 12x 4 . Hence f (g(x)) = g(f (x)). 9 Decomposing y = f (x) = 18x 4 . A case-deﬁned function The function f (x) might change its expression across various domains. For example, f (x) may be a linear function when x takes negative values (x < 0), but quadratic otherwise (x ≥ 0).