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Doreen has preferences represented by the utility function U(x,y)=10x+5y. She consumes 7 units of good x and 4 units of good y. If her consumption of good x is lowered to 2, how many units of y must she have in order to be exactly as well off as before?

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Related questions

Consider an individual whose utility function is U = X0.5Y0.5. If the individual consumes 1 unit of X and 4 units of Y, then she will experience some level of utility. If the individual instead consumes 2 units of Y, how much of good X must she consume in order to attain the level of utility associated with 1 unit of X and 4 units of Y?

5. Suppose Ann consumes only X and Y and her utility is given by U(X, Y) = min (3X, 5Y). The price of X is , and the price of Y is . She has income I = $90 to spend on X and Y

(a) Are good X and good Y perfect substitutes or perfect complements? Why?

(b) Write down the consumption ratio of good X and good Y.

(c) Write down the budget constraint.

(d) What is the consumption bundle to maximize the utility level? What is the maximum utility level?

Sally the Sleek's preferences can be described by the utility function U(x,y) = x^2y^3/512. Prices are px = 2 and py = 6; she has an income of $80 to spend.

(a) If Sally initially consumed 4 units of x and 12 units of y, how much additional utility does she get from spending one (small fraction of a) dollar more on good x? How much additional utility does she get from spending one (small fraction of a) dollar more on good y?

(b) By how much would her utility change if she stayed on the same budget and consumed 4 (small€) dollars worth more of x? Judging from this, can the allocation of x = 4 and y = 12 be optimal?

(c) How much should Sally consume of x and y in order to maximize utility, given her income?

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