When a company conducts a stock$$ split, it exchanges new shares for old ones according to some ratio. For$$ example, in March$2018,$ Herbalife conducted a$$ two$-$for$-$one stock$$ split, so after the split each shareholder received two new shares in exchange for each share owned before the split. A stock split increases the number of shares outstanding but changes nothing else about the value of the$$ company, so a split results in a proportionate decline in the per share stock price. In$$ Herbalife's case, the price before the$$ two$-$for$-$one split was $$$$112\mathrm{.}46,$ and the day after the split the price was $$$$54\mathrm{.}38,$ roughly$($though not$$ exactly$)$ a $50\%$ drop.

a$.$ Suppose a company that is part of the DJIA engages in a$$ two$-$for$-$one stock split and immediately after the split its stock falls by $50\%,$ leaving the total value of the company unchanged.$$ Conceptually, what impact should this split have on the$$ DJIA?

b$.$ When this split$$ occurs, all else held$$ constant, what happens to the numerator of Equation $3\mathrm{.}1$ LOADING...$?$

c$.$ When this split$$ occurs, all else held$$ constant, what do you think happens to the denominator of Equation $3\mathrm{.}1$ LOADING...$?$