A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = min{αx, y} with α > 0. The prices of the goods are px = 2 and py = 1. The consumer has an income of I > 0. (a) For what values of α is this utility function strictly monotone? (b) For what values of α will the consumer demand (i.e., Walrasian demand) be more x than y? (c) For what values of α will the consumer spend more on x than y (given her Walrasian demands)? (d) If x is bicycle tires and y is bicycle frames, then what is the reasonable value for α? Given px, py and this value of α, what is the minimum cost of obtaining a utility u = 1? What are the demands that solve this expenditure problem?
Please answer all the questions below.
A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = min{αx, y} with α > 0. The
(a) For what values of α is this utility function strictly monotone?
(b) For what values of α will the consumer
(c) For what values of α will the consumer spend more on x than y (given her Walrasian demands)?
(d) If x is bicycle tires and y is bicycle frames, then what is the reasonable value for α? Given px, py and this value of α, what is the minimum cost of obtaining a utility u = 1? What are the demands that solve this expenditure problem?
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