When a company conducts a stock split, it exchanges new shares for old ones based on a predetermined ratio. For example, in February 2019, Ajinomoto Co. conducted a two-for-one stock split so that 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. In Ajinomoto’s case, the price before the two-for-one split was ¥1,700, and it became ¥852 after the split, roughly a 50% drop. 

a. Suppose a company that is part of Nikkei 225 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 Nikkei 225?
b. When the split occurs, all else held constant, what happens to the numerator of Equation 3.1?
c. When the split occurs, all else held constant, what do you think happens to the denominator of Equation 3.1?
d. How would your answers to all three questions above change if a company in the TOPIX Index conducted a two-for-one stock split?