Arya Stark wishes to derive optimal utility from consumption bundle

(1, 2). Suppose her utility function and budget constraint is given as

U(12) = 1

1/3

2

1/3

and 11 + 22 = M respectively. Required;

i. State Arya's choice problem. (2 Marks)

ii. Derive the optimal demand functions for good 1 and 2. What is the name of these

demand functions? (8 Marks)

b) Discuss the shutdown rule of perfectly competitive firms. (6 Marks)

c) Distinguish between returns to scale and marginal rate of technical substitution.

(4 Marks)