More. We are using data on executive compensation and profits of 70 companies. Suppose the following model describes the relationship between executive compensation (compensation) (in $ millions) and the company profits (prof it) (in $ millions): log(compensation) = 0.16 + 0.00127prof it
(a) What is the executive compensation when prof it = 100? When prof it = 500? (Hint: you will need to exponentiation.)
(b) What is the percentage increase in compensation when prof it increases by 400 ($ millions).
(c) Use the results of part(a) to compute the exact percentage difference in compensation when prof it = 500 and proof it = 100. Comment on how this compares with the approximation in part(b).
(d) Now, we suppose the following model describes the relationship between (compensation) and (prof it): compensation = 0.16 + 0.00127 × prof it − 0.0001 × prof it2 Calculate the partial (marginal) effect of prof it on compensation.