A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y. a) Determine this consumer’s current utility level. b) Compute the consumer’s marginal utilities of goods X and Y. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X. d) Determine this consumer’s optimal consu
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y. a) Determine this consumer’s current utility level. b) Compute the consumer’s marginal utilities of goods X and Y. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X. d) Determine this consumer’s optimal consu
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.
a) Determine this consumer’s current utility level.
b) Compute the consumer’s
c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa?
The consumer’s marginal rate of substitution is MRS = Y/X.
d) Determine this consumer’s optimal consumption of both goods.
e) By how much does the consumer’s utility increase when she consumes the optimal bundle?
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