A consumer likes to consume ice cream in a mixture of 3 scoops of vanilla (v) and one scoop of strawberry (s) and does not want to consume any vanilla or strawberry ice cream by itself. (a) Draw the consumer's indifference curves and write his utility function. Assume he receives three utils from each mixture. You can put the vanilla ice cream on the vertical axis and the strawberry ice cream on the horizontal axis. (b) Suppose that the consumer has $32 per month allocated to ice cream consumption. Assume the price of vanilla ice cream is p = $4, and strawberry ice cream is ps $4. What is his optimal allocation for vanilla and strawberry ice cream? How much utility does he get from this allocation? There is a shortage in vanilla, resulting in p = $8. What is the new consumption bundle? (d) Using Hicksian decomposition, find this price change's substitution and income effects. (e) The consumer's roommate has ice cream preferences given by u(v, s) = 0.5 ln (v) + 0.5 ln (s). Suppose his ice cream budget is also $32, and he faces the exact price change. What would be the income effect and the substitution effect in her case? (f) What is the welfare implication of this price increase on each consumer? (g) Their friend wants to give them ice cream as a gift and was wondering if to give a cash or ice cream gift. What would you suggest to him? Consider the following utility u(x, 2; ) = (x -)x2 with a + 3 = 1, 0 < a, 3 < 1, and r > 0. The utility will be positive if r2 r and T20. Assume the utility is zero for r