Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)

Using Stata command power x, diff(y) sd1(s1) sd2(s2), which computes the total sample size required to detect an experimental-group mean that’s y units different from the control-group mean of x. This test assumes that the standard deviations of the two groups are s2 and s1, respectively, that a two-sided test with a 5% significance level will be used, a power of 80%, and that both groups will have the same number of observations (the defaults).
In this case, x would capture the average required return on equity reported in Question 2 by individuals in the control group, and y would capture the difference from this mean among agents in a particular treatment group.
power twomeans .09, diff(.03) sd1(.050) sd2(.050): N per group = 45
power twomeans .09, diff(.03) sd1(.045) sd2(.045): N per group = 37
power twomeans .09, diff(.03) sd1(.040) sd2(.040): N per group = 29
power twomeans .09, diff(.03) sd1(.035) sd2(.035): N per group = 23
power twomeans .09, diff(.02) sd1(.050) sd2(.050): N per group = 100
power twomeans .09, diff(.02) sd1(.045) sd2(.045): N per group = 81
power twomeans .09, diff(.02) sd1(.040) sd2(.040): N per group = 64
power twomeans .09, diff(.02) sd1(.035) sd2(.035): N per group = 50
power twomeans .09, diff(.01) sd1(.050) sd2(.050): N per group = 394
power twomeans .09, diff(.01) sd1(.045) sd2(.045): N per group = 319
power twomeans .09, diff(.01) sd1(.040) sd2(.040): N per group = 253
power twomeans .09, diff(.01) sd1(.035) sd2(.035): N per group = 194
Note: these power calculations hold for different values of x, e.g., x = 6, 7, 8, 9, 10, 11, 12, etc.