\\ 44 u; 1. The maximisation of a standard CobbDouglas function U(:rl , $2) = :r'frc' under a generic budget constraint leads to the following optimal solutionJ which also correspond to demand functions for the two goods (see Bowles and Halliday, p. 357): $1 = 101 (1) _ {1 (rjm $2 P2 (2) (a) What happens to the demand for :01 and :32 if the income and the two prices are all doubled? How do you interpret this result? (13) Let's assume that o; = 1/2 and the consumer income is 30. The prices are originally set at p1 = 3 and pg = 6. What is the consumer demand? (c) Because of a sudden decrease in supply, the price of good 1 decreases to p1 = 2. What is the new consumer demand? Represent the solutions graphically and decompose the change in demand in terms of substitution elTect and income effect. (d) Compute and interpret the price and the income elasticities of de mand for the two goods. Compute the crossprice elasticity of de mand. How does the decrease of p1 impact the different elasticities