Suppose a consumer called Jack only consumes two goods with a utility function U(x, y) =...

 

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Suppose a consumer called Jack only consumes two goods with a utility function U(x, y) = logr+logy where log is the natural logrithm; x and y denote (the amount of) the two goods being consumed. Let the initial prices of the two goods be p = $10, Py = $4, and his income m = $1000. 1. Let's call his utility-maximizing basket (x, y), and the maximized utility u, what are they equal to? (3 points) 2. Now suppose price of y has dropped to p = $1, and his utility-maximizing basket becomes (B, UB), what is it equal to? (2 points) 3. With this new set of prices, suppose Jack's income has changed to m' in such a way that he would retain his original utility level u. What is his utility-maximizing basket (x,y) in this case equal to? (4 points) 4. What is the substitution effect, income effect, and total effect in terms of the changes in the utility-maximizing baskets. (3 points) 5. In one diagram, illustrate your answers to the above 4 questions in a (x-y) commodity space with appropriate labels. (8 points) 1 6. In a different diagram, draw Jack's demand curve with respect to the y commodity, using some of the above results. Is y a Giffen good? Explain. (5 points) Suppose a consumer called Jack only consumes two goods with a utility function U(x, y) = logr+logy where log is the natural logrithm; x and y denote (the amount of) the two goods being consumed. Let the initial prices of the two goods be p = $10, Py = $4, and his income m = $1000. 1. Let's call his utility-maximizing basket (x, y), and the maximized utility u, what are they equal to? (3 points) 2. Now suppose price of y has dropped to p = $1, and his utility-maximizing basket becomes (B, UB), what is it equal to? (2 points) 3. With this new set of prices, suppose Jack's income has changed to m' in such a way that he would retain his original utility level u. What is his utility-maximizing basket (x,y) in this case equal to? (4 points) 4. What is the substitution effect, income effect, and total effect in terms of the changes in the utility-maximizing baskets. (3 points) 5. In one diagram, illustrate your answers to the above 4 questions in a (x-y) commodity space with appropriate labels. (8 points) 1 6. In a different diagram, draw Jack's demand curve with respect to the y commodity, using some of the above results. Is y a Giffen good? Explain. (5 points)

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1 Jacks utilitymaximizing basket AA is equal to x 99010 99 and y 104 25 His maximized utility u is e... View the full answer