Ben receives utility from consuming two goods x and y as given by the utility function U=x2y4. The marginal utility Ben receives from x and y are…

Ben receives utility from consuming two goods x and y as given by the utility function U=x2y4. The marginal utility Ben receives from x and y are given as follows: MUx=2xy4; MUy=4x2y3. Ben has income I and the price of the goods are px and py respectively. Suppose Ben’s income is at I=300 and the price of good y is py=2.

a. What is Ben’s marginal rate of substitution of y for x (MRSxy)?

b. Derive Ben’s demand function for good x.

c. The price of x is currently at px=1. How many x and y will Ben consume to maximize his utility? Draw Ben’s indifference curve and budget constraint in a well-labelled diagram and identify the optimal bundle.

d. Suppose price of x rises to px=2. What is Ben’s new optimal bundle? Draw his new budget constraints in the above diagram and illustrate the new optimal bundle.

 
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