Mathematics for Finance

1. Assume that demand for goods (Q) depends on its own price (P), income (M) and the price of a substitute goods (S) according to the demand function
Qi= (B1)(Pi) + (B2)(Mi) + (B3)(Si)
where B1, B2 and B3 are parameters whose values are not yet known and the
subscript i denotes the observation number. Three observations of the amount Q demanded when P, M and S take on different values are shown belows:

Observation No.1: P=6, M=5, S=5, Q=4
Observation No.2: P=8, M=8, S=6, Q=6.4
Observation No.3: P=5, M=6, S=4, Q=5.1


(a) Find teh values of B1, B2 and B3 by setting up teh relevant system of simultaneous equations in matrix format and solving using the inverse matrix.
(b) Use the vector of parameters (b1, B2, B3)^T that you have found to predict the value of Q when P, M and S take the values 7, 9 and 10, respectively, by vector multiplication.