a. Show that the CES functionU= aX/&+BY/8 is homothetic. How does the MRS depend on the...

 

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a. Show that the CES functionU= aX/&+BY/8 is homothetic. How does the MRS depend on the ratio y/x? b. Show that your results from part (a) agree with our discussion of the cases ô=1 (perfect substitutes) and ô =0 (Cobb-Douglas). c. Show that the MRS is strictly diminishing for all values of &< 1. d. Show that if x=y, the MRS for this function depends only on the relative sizes of a and B. e. Calculate the MRS for this function when y/x =0:9 and y/x=1:1 for the two cases & =0:5 and 8 = -1. What do you conclude about the extent to which the MRS changes in the vicinity of x= y? How would you interpret this geometrically? a. Show that the CES functionU= aX/&+BY/8 is homothetic. How does the MRS depend on the ratio y/x? b. Show that your results from part (a) agree with our discussion of the cases ô=1 (perfect substitutes) and ô =0 (Cobb-Douglas). c. Show that the MRS is strictly diminishing for all values of &< 1. d. Show that if x=y, the MRS for this function depends only on the relative sizes of a and B. e. Calculate the MRS for this function when y/x =0:9 and y/x=1:1 for the two cases & =0:5 and 8 = -1. What do you conclude about the extent to which the MRS changes in the vicinity of x= y? How would you interpret this geometrically?

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