Suppose that a rock star gives concerts. The production function of the concert is the following: Q(C,A,G) = (C – 10)'/ªA/4G/4 | where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman and G represents hourly contribution of guitarist George. a) If Chris has 26 units of hours, is there increasing returns to scale in production of concerts? b) Assume George has fixed amount of hours, G=16, and hourly wage of G is 5. Denote the wage of Chris= r and the hourly wage of Ataman =w. Derive Rock star's demand for inputs-C and A, respectively-as a function of output (Q). c) Assume that George has fixed amount of hours G=16 and hourly wage of G is 5. Additionally, you are given that the wage of C = r=100 and the unit wage of Ataman=w=100. Show that Rock star's short run cost function is given by TC(Q) = 1000 +50Q²-
Suppose that a rock star gives concerts. The production function of the concert is the following: Q(C,A,G) = (C – 10)'/ªA/4G/4 | where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman and G represents hourly contribution of guitarist George. a) If Chris has 26 units of hours, is there increasing returns to scale in production of concerts? b) Assume George has fixed amount of hours, G=16, and hourly wage of G is 5. Denote the wage of Chris= r and the hourly wage of Ataman =w. Derive Rock star's demand for inputs-C and A, respectively-as a function of output (Q). c) Assume that George has fixed amount of hours G=16 and hourly wage of G is 5. Additionally, you are given that the wage of C = r=100 and the unit wage of Ataman=w=100. Show that Rock star's short run cost function is given by TC(Q) = 1000 +50Q²-
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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Transcribed Image Text:Suppose that a rock star gives concerts. The production function of the concert is the following:
Q(C,A,G) = (C – 10)'/4A/4G/4
where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman
and G represents hourly contribution of guitarist George.
a) If Chris has 26 units of hours, is there increasing returns to scale in production of concerts?
b) Assume George has fixed amount of hours, G=16, and hourly wage of G is 5. Denote the wage of
Chris= r and the hourly wage of Ataman =w. Derive Rock star's demand for inputs-C and A,
respectively-as a function of output (Q).
c) Assume that George has fixed amount of hours G=16 and hourly wage of G is 5. Additionally, you are
given that the wage of C = r=100 and the unit wage of Ataman=w=100.
Show that Rock star's short run cost function is given by TC(Q) = 1000 +50Q²-
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