Problem I Last week, neither Alistair nor purchased blueberries Both consumers had to spend on blueberries and/or raspberries the price Of the two fruits Was per pack and both consumers bought raspberries Alistair's utility for blueberries and raspberries is = x utility for blueberries and raspberries is x + 121n(y)_ a) In tW'O graphs, illustrate Alistair'S and optimal Choices. Your graphs t illustrate the consumers' budget Constraints and their indifference Curves at the optimal bundle. b) At optimal bundle, What is Alistair's marginal rate Of substitution Of raspberries for blueberries At their bundle, What is rate Of week, blueberries COSI per pack just like last raspberries COSt per pack. HOW many packs Of blueberries and raspberries Will Alistair buy this week? Clearly iustify your Using the method, find hOW many packs Of blueberries and raspberries Will buy this rite the n o f the ra lover 's functio n _ Take the respect to x , reSlNCt to y, and respect to (first order conditions Of the problem) and equate them to c. Solve for the endogenous v y, and DO you find acceptable (non-negative) for variables? NOW compute utility from extra dollar spend on blueberries her marginal utility from an dollar Spent on raspberries Contrast and Compare these values and the value you Obtained for the part d) c_ What is the lowest price for raspberries that would convince Alistair to spend Some money on blueberries? Problem 2 Another instance When people are likely not to spend a dime (or a minute) on an item is When they have a dislike for mixing the item With Other items In this Case, We Say the Consumer has preferences' and indifference curves bowed out front the In plain language, the consumer has a preference for We Often feel this Way our favorite social C_onsider a kid Who has four hours a day to spend on social media. They spending time on Snapchat (x) or spending time o n Twitter a) W rite the kid time cons train t and it in a graph Where you measure time SIX n t o n at along the time Spent on along the vertical axis. kid'S utility from time SENnt on Snapchat and time SENnt on Twitter is = 4x2 + In graph, draw couple Of the kid'S Indifference curves. Notice how the kid'S increases along each curve as he spends more time on Snapchat less on Twitter. Geometrically, find the kid'S optimal time-allocation, that IS the point on the kid ' S time constraint that lies on the highest possible indifference curve _ Does the kid spend any on Twitter? Last, Check that the method fail to find the correct optimal time allocation. W rite the function. n firs t by the time Constraint by negative rite the first order for the to x, to y, and to to zero) and solve. Do you find acceptable values for x, y and Why do you think they are the wrong ones?