2. Suppose Deb has the following utility function for goods x and y: u(x, y): =...

 

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2. Suppose Deb has the following utility function for goods x and y: u(x, y): = (x + Iny) ². For all the following questions, show all steps of calculations, spell out all the assumptions behind your answer, etc., to receive full credit. A correct answer without complete work and explanations will receive partial credit. a) Derive Marshallian demand functions for x and y for the above utility function. (10 points) b) Suppose M = 100, Px = 4, and Py = 2. Use these values of M, Px, and Py to compute the numerical values of the Marshallian demand functions for x and y that you derived in part (a). (4 points) c) Suppose P. drops to 2 while M = 100 and Py = 2. Compute the total change in the demand for good x (or the total effect) due to a fall in the price of good x. (5 points) d) Compute the change in the demand for good x solely due to the substitution effect and the income effect due to a fall in the price of good x. (6 points) e) Compute the value of Deb's utility function after the drop in the price of good x? Has Deb's utility increased, decreased, or stayed the same after the fall in the price of good x? (5 points) 2. Suppose Deb has the following utility function for goods x and y: u(x, y): = (x + Iny) ². For all the following questions, show all steps of calculations, spell out all the assumptions behind your answer, etc., to receive full credit. A correct answer without complete work and explanations will receive partial credit. a) Derive Marshallian demand functions for x and y for the above utility function. (10 points) b) Suppose M = 100, Px = 4, and Py = 2. Use these values of M, Px, and Py to compute the numerical values of the Marshallian demand functions for x and y that you derived in part (a). (4 points) c) Suppose P. drops to 2 while M = 100 and Py = 2. Compute the total change in the demand for good x (or the total effect) due to a fall in the price of good x. (5 points) d) Compute the change in the demand for good x solely due to the substitution effect and the income effect due to a fall in the price of good x. (6 points) e) Compute the value of Deb's utility function after the drop in the price of good x? Has Deb's utility increased, decreased, or stayed the same after the fall in the price of good x? (5 points)

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