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
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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Answer questions A-E. Show all work. See attached image.
Transcribed Image Text: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 (think about this is as a market rate for the per-hour compensation
2
that he would receive for managing another firm, or a compensation for the sacrificed leisure). The
production technology the firm uses to produce output at time t is
Yt = AKLE
where 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. Imagine
that the firm chooses strictly positive amounts of capital and labor, and zero entrepreneurial
effort, E 0. Show that this is never optimal and the firm should optimally choose a strictly
positive 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.
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