By Martin Anthony, Norman Biggs

With no anticipating any specific heritage of the reader, this booklet covers graphs and kin, sequences and boundaries, partial derivatives, optimization, vectors and matrix algebra. all through, the strain is firmly on how the maths pertains to economics.

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Extra info for Mathematics for Economics and Finance: Methods and Modelling

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The subset ~~ consisting of those points for which x and yare both nonnegative is sometimes known as the first quadrant. This set is particularly relevant in economics because it represents realistic values of the coordinates; for example, in a 'supply and demand' diagram, neither q (quantity) nor p (price) can be negative. 2 Functions Given two arbitrary sets A and B, a function from A to B is a rule which assigns one member of B to each member of A. For example, if A and Bare both the set ~, the rule which says 'multiply by 2' is a function.

This gives the equation x 2 - 5x + 6 = 2x - 6, that is x 2 - 7x + 12 = O. Here the quadratic expression factorises x 2 - 7x + 12 = (x - 4)(x - 3), and the solutions are Xl = 4 and X2 = 3. The corresponding y-coordinates are obtained by substituting in either of the original equations, giving YI = 2 and Y2 = o. 4c. 1 Suppose that the supply and demand sets for a good are given by S = {(q,p) I q - p = -7}, D = {(q,p) I q + 3p = 10}. Determine the supply function, qS, the demand function, qD, the inverse supply function, pS, and the inverse demand function, pD.

95 and b = N (assumed to be a fixed constant). 9S)t. The term 20N is constant and does not vary with time. 9SY decreases with t. 95Y decreases, approaching zero, this will be true precisely when the constant factor (30000 - 20N) is positive. Thus we require 30000 - 20N > 0, or N < 1500. Since N is an integer, this condition becomes N ~ 1499. Therefore, if the Euro-commissioner manages to negotiate a value of N no larger than 1499, she will ensure victory. The final part of the problem concerns what happens if the commissioner manages to negotiate a value of N as low as 1300.

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