a. Thomas derives utility from only two goods, Clothes (C) and Food (F). His utility function is given as follow: U(C,F) = 6LogC + 12logF The marginal utility of a unit of clothes (MUC) and food (MUF) are given as follow: 6 12 MU == MUF C F Thomas has an income of $1200. The prices of clothes (Pc) and food (PF) are $40 and $80 respectively. i. Derive Thomas's budget constraint. 11. What quantities of clothes and foods will maximize Thomas's utility? 111. Holding the price of food at $80 and income at $1200, derive Thomas's demand curve for clothes. Discuss the relationship between P and C b. Sandy is a strange person who loves risky gambles. Her utility function is given as follow: U = W² where W is her wealth. She has joined a game which there is 30% chance turns her wealth to $100 and 70% turns her wealth to $10. i. ii. What is the expected utility to Sandy from this gamble? Suppose she is offered another alternative game which 100% turns her wealth to $40, would she accept this new game or stick to the previous game?