Answer questions A-E. Show all work. See attached image. Consider an entrepreneur who owns a firm which uses capital K and labor L, supplied at rentalrater and wage w. Apart from this, operating the firm requires entrepreneurial effort E (say thenumber of hours that the entrepreneur has to spend operating the firm). The entrepreneur valueseach hour of his time at (think about this is as a market rate for the per-hour compensation2that he would receive for managing another firm, or a compensation for the sacrificed leisure). Theproduction technology the firm uses to produce output at time t isYt = AKLEwhere parameters a, ß, y are all strictly positive and a + B + y ≤ 1(a) Express the growth rate of output Y, as a function of the growth rates of individual inputs.(b) Set up the problem of a profit maximizing firm that chooses all three factors of production,and needs to pay them at competitive rates, including entrepreneurial effort (from now on,feel free to drop the time indices).(c) Write down the first-order condition with respect to the entrepreneurial choice. Imaginethat the firm chooses strictly positive amounts of capital and labor, and zero entrepreneurialeffort, E 0. Show that this is never optimal and the firm should optimally choose a strictlypositive amount of E.(d) Show that the share of output that goes to the entrepreneur is equal to y(e) Does the firm in this problem earn zero economic profit? Explain rigorously why or why not.

Production function : Yt = A Ktα Ltβ Etγ Cost per unit capital = r Cost per unit of labor = w…

Consider an entrepreneur who owns a firm which uses capital K and labor L, supplied at rental rater and wage w. Apart from this, operating the firm requires entrepreneurial effort E (say the number of hours that the entrepreneur has to spend operating the firm). The entrepreneur values each hour of his time at c (think about this is as a market rate for the per-hour compensation 2