Question

It is assumed that consumption C depends on income Y and that this relationship takes the form of the linear function C= a + bY. When Y is N100, C' is observed to be N305. When Y is N150, C is observed to be N455. What are the values of a and b in this function?

Answer 1

$305 = a + b100 \\ 455 = a +b150 \\ a = 305-100b \\ 455 = 305 -100b+150b \\ 455-305=150b-100b \\ 150 = 50b \\ b= \frac{150}{50}=3 \\ 305 = a + 3 \times 100 \\ 305 = a +300 \\ a = 305-300 = 5$

So, a= 5 and b=3