solution to quiz2

solution to quiz2 - Bora Kim(2924798272(Quiz 2 Econ 318...

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Bora Kim (2924798272) ( Quiz 2 Econ 318 ) Problem 1 You are interested in the relationship between output (Q), Capital, and Labor. Q = β 0 + β 1 Ln ( Capital ) + β 2 Labor + β 3 Labor 2 + u ˆ Q = - 1 . 5 + 44 . 2 Ln ( Capital ) + 1 . 28 Labor - 0 . 032 Labor 2 (a) How do you interpret parameter of Ln(capital)? (ans) ˆ β 1 = 44 . 2 and ˆ β 1 / 100 = 0 . 442 shows that 1 percent increase in capital increases the output by 0.442 units. (b) At what level of labor does output reach its maximum? Calculate maximum output when capital= 10. (ans) Since ˆ Q ∂Labor = 1 . 28 - 0 . 032 * 2 * Labor = 0 when Labor = 1 . 28 2 · 0 . 032 = 20, the output reaches its maximum when labor level is equal to 20. Maximum output when labor=20 and capital=10 is - 1 . 5 + 55 . 2 * log (10) + 1 . 28 * 20 - 0 . 032 * 20 2 = 113 . 07 . Problem 2 In the following multiple regression model dependent variable, ln ( Inc ) is natural log of income for rickshaw drivers in Calcutta India and the independent variables are age and IQ. The unknown parameters are β s. Ln ( Inc ) = β 0 + β 1 IQ + β 2 age + u, u has a normal distribution OLS, using 32 observations, Dependent variable: Ln(Inc) coefficient std. error const 0.01557 0.36823 IQ 0.08611 0.02376 age 0.09818 0.04181 Sum squared resid=35.5 S.E. of regression=1.1833 R-squared=0.7802 (a) You are interested in constructing a 95% prediction interval (for Ln(Inc)) for a 30 year old rickshaw driver with IQ of 100. Your friend suggests that estimating the following model will provide you with the predicted value: Ln ( Inc ) = θ 0 + β 1 ( IQ - 100) + β 2 ( age - 30) + u. Using the following estimated model, demonstrate that your friend is correct and construct and interpret the interval.

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