Answer all parts (a)-(d) of this question.There are two goods in the economy: good x and good y with prices px and py, respectively.Alice has an income of m.Suppose first that her utility function isu(x, y) = √x +√y.(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences curves.(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.Suppose now instead that Alice had another utility function, namelyv(x, y) = x2 + y2. (1)(d) [15 marks] Derive Alice’s demand function with the utility function v, as specified inequation (1) above.
Answer all parts (a)-(d) of this question.There are two goods in the economy: good x and good y with prices px and py, respectively.Alice has an income of m.Suppose first that her utility function isu(x, y) = √x +√y.(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences curves.(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.Suppose now instead that Alice had another utility function, namelyv(x, y) = x2 + y2. (1)(d) [15 marks] Derive Alice’s demand function with the utility function v, as specified inequation (1) above.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Answer all parts (a)-(d) of this question.
There are two goods in the economy: good x and good y with prices px and py, respectively.
Alice has an income of m.
Suppose first that her utility function is
u(x, y) = √
x +
√
y.
(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences
(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.
(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.
Suppose now instead that Alice had another utility function, namely
v(x, y) = x
2 + y
2
. (1)
(d) [15 marks] Derive Alice’s
equation (1) above.
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