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3. (35 points). Matilda likes Coke, denoted by C, and Pepsi, denoted by P. Her utility function for the two goods is equal to U (C,P) = 9C + 3P . The price of both goods is equal to $1, and Matilda has $20 to spend. a) Derive Matilda's optimal consumption bundle. b) Suppose the price of Coke increases to $2. Derive Matilda's optimal consumption bundle. Decompose the change in her consumption of Coke into the substitution and income effect. Comment on your result. c) Suppose the price of Coke increases to $4. Derive Matilda's optimal consumption bundle. Decompose the change in her consumption of Coke into the substitution and income effect. Comment on your result