2. Answer all parts (a)-(d) of this question. There are two goods in the economy: good z and good y with prices pz and py, respectively. Alice has an income of m. Suppose first that her utility function is u(x, y) = √x + √ÿ. (a) [10 marks] Derive and illustrate in a graph Alice's indifferences curves. (b) [15 marks] Derive Alice's optimal bundle when pz = 2, Py = 4 and m = 24. (c) [10 marks] Derive Alice's optimal bundle when p. 8, p = 2 and m = 24. Suppose now instead that Alice had another utility function, namely v(x, y) = x² + y². (1) (d) [15 marks] Derive Alice's demand function with the utility function v, as specified in equation (1) above.
