. How do you test for constant returns to scale in a Cobb-Douglas production fun
ID: 1102413 • Letter: #
Question
. How do you test for constant returns to scale in a Cobb-Douglas production function of the form y, = Ax"AXA exp(u), i = 1, , N , where y-output produced and the x's correspond to various inputs employed? 9. Let p, equal the price of a stock (say Exxon) and SP500, be the price of a market ind like the S&P; 500 index. How do you use a logarithmic transformation to approximate the rat return on the stock (R.) and the rate of return on the market index (R)? 10. You hypothesize that faculty wages at Big State University depend on the amount of experience an individual has and also whether or not the person is a member of the College o Business. You estimate the model wage,-B+Bexperience, +B,CB,+B,(e xperience, x CB)+u, where CB-1 if the person is member of the College of Business and 0 otherwise. The estimated coefficients from your m areA-50,000, A-1000, .-1500, .. 250. Dothese coefficients support your hypothesis? Briefly explain. 11. You hypothesize a quadratic relation between x and y. Your model takes the form y,-A+Bx, + , +4.jzl, ,N. You obtain estimatesA--15 andA-+0.75. At w value of x does your function reach its turning point? At the turning point did your function reach a minimum or a maximum?Explanation / Answer
We will run a log- log transformation model for this .Now our model will be like
lnYi =b0+b1lnX1i+b2 lnX2i +b3ln X3i +....+bkln Xki
We will Check for the null hyopothesis that
H0: b1+b2+b3+....+bk =1
H1: b1+b2+b3+...+bk !=1
Using t-statistic . If t-calculated > t-critical, We will reject the null hypothesis that funcion exhibits constant returns to scale else we will no reject the null.
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