A continuous function g : [a, b] + [a, b] must have at least one fixed point, that is, at least one solution x e [a, b] for the equation x = g(x). This is an immediate consequence of the intermediate value theorem (see Lecture 6, page 3). If in addition, we would like to prove that the fixed point is unique, that is, there is exactly one solution for x = g(x), then one useful result is the so-called contraction mapping theorem that says: if there exists 1 € (0, 1) such that g(x) – g(y)<\x – y for all x, y € [a, b], then the fixed point is unique. Moreover, the fixed point recursion Xk+1 = g(xx) starting from any initial guess xo € [a, b] will converge to this unique fixed point as k → 0. (a) Kepler's equation in celestial mechanics is of the form: x = m + esinx, where e, m are known g(2) parameters, and one would like to solve for the fixed point x, which physically represents "eccen- tric anomaly" - an angular variable that defines the position of a planet moving along an elliptic orbit. The known parameters satisfy 0

the benefits of raising bc’s minimum wage to $15 through a

series of pre-announced staged increases far outweigh the likely

costs. claims that such an increase will lead to massive job losses

in low-wage sectors of the economy are not credible.

• an increase to $15 would result in some job losses. however,

the likely impact is less than a 1 per cent reduction in the overall

provincial employment rate, and a 7.6 per cent reduction in the

employment rate for those currently making between $10.25

and $15 per hour.

• the large job loss impacts predicted by some opponents of

minimum wages misrepresent the existing economic research. in

reading and using that research, it is important to recognize that

estimates showing job loss effects of minimum wage increases

apply only to teenagers. estimated effects for young adult and

adult workers range from insignificant to non-existent.

• focusing on teenage workers plays up an inaccurate stereotype

about who earns very low wages in bc and leads to exaggerated

claims about job losses. only 26 per cent of those currently making

between $10.25 and $12 are teenagers, and only 5 per cent

of those making between $12 and $15 are teenagers.