Indicate whether the statement is true or false, and justify your answer. State any additional assumptions you may need.

a$.$ The RAND study was especially useful for measuring price elasticities because it randomly assigned insurance plans to participants $($as opposed to letting them choose$).$

b$.$ An hour spent exercising always pays for itself by decreasing the time spent sick by more than an hour.

c$.$ People who drop out of high school are able to produce more health than college graduates because they have more free time to invest in health production.

d$.$ Consider two investment streams w and z which pay out some amount, w$($t$)$ and z$($t$),$ in each period t$.($The amount may be negative in some periods$).$ If the interest rate is exactly equal to the internal rate of return of w$($t$),$ the net present value of choosing w over z is zero.