Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility?
Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U).
Have you found a true maximum? Explain your answer.
Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples
and bananas are p. = 7 and pb - 7. Which of the following utility functions over
quantities of apples (a) and bananas (b) could represent Rafe's preferences?
=
u(a, b)-a4/5 61/5
Ou(a, b) = a¹/5 64/5
Ou(a, b)-a2/3 b1/3
Ou(a, b)-a¹/3 2/3
Two friends, Minrui and Jing, share a flat and both consume internet (i) and all other goods (g). The
utility function for Minrui is U_m=i^(0.3)g^(0.7) whereas the utility function for Jing is U_m=i^(0.1)g^(0.9).
Considering that the income of both individuals are the same $500 and that the prices are p_i = $80
and p_g = $5, what would be the optimal allocation of public good (i) and private good (g)? Interpret
your answer.
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