Part 2 [20 marks] Consumption decisions often depend on more than just the price ofgoods. They can also depend on the non- monetary costs involved in purchasing, storing. and consuming a good. Also important is that not all money must be spent on a good, even if it has a low price; money can give utility, as it can be spent on different goods outside of one specific market. I propose the following model: Utility = Beer'\"Time'3 + aid/Money Where Time is the free time you have left after consuming/storing a number ofbeers and Money is the cash you have left after buying your beer. Suppose there are 3 types ofpeople, who differ in how much they value their beer and how much they value their money. They also differ in how much money and time they have. {ne A has or = 0.5, B = 0.5, and it = 5. 1er B has a : 0.7, B : 0.3, and it: 5. Both A and B have $50 and 8 units of Time. 1er C has or : 0.3, B : 0.7, and 7t : 10. They value their money highly as they have so little of it due to not working [they are unemployed or retired?) They have a lot of "ee time. Type C people have $10 and 24 units of Iime. In a market with 50 people of each type [150 total], a monopoly producer ofbeerwishes to make the most prot possible. Their Marginal Cost is $1 per beer. 1.{15 marks]- Don't try and solve this using calculus. a] Beer costs consumers 1 unit of Time per bottle. When beer costs $2, compare the utilities for Types A, B, and C when choosing between 0, 1, 2, and 3 beers. Each group will choose to consume the amount that gives them the highest utility. (5 marks] (Hint: No beer gives Utility of 35.355 for Type As. Three beers gives Utility of 37.039 for Type As] b] At $3 beers, do the same for the choice between 0, 1, and 2 beers. Do this again for $4, $5, $6, and $7 beer, as long as a group's consumption choice is non-zero. Calculate the firm's prots at these different prices. $4 beer should bring in the most prots {3 marks] c] Suppose the rm offers a six-pack ofbeer for $10. It costs 6 units of Time. If single bottles ofbeer cost $4, which of the 3 types will purchase the six-pack? [Compare the Utility of 6 beers to the utility of their preferred choice in [b] at $4]. What if the six-pack costs $11?{3 marks] d] If the rm charges $7 for individual beers, and $11 for the six-pack, what is their prot? {2 mark] e] In the previous case, Type C has left the market. To bring them back, the firm creates a very time- consuming coupon: the price of beer falls to $4 for those willing to use the coupon, which increases the Time cost of each and every beer to 6 units 'om 1 unit. Compare the utility of 1 beer at $4 with this couponto no beer for all 3 types. [ftype C is the only group to purchase beer, the coupon works and prot will rise even higher than in [d]. {2 marks] 2.{5 marks} Don't try and solve this using calculus. a] With 50 people of each type, suppose you attempted to implement Block Pricing. What is the maximum prot you can attain ifyou sold only 2-packs without giving the option to buy singles or six-packs?{3 marks] b] What is the maximum prot you can achieve with any pricing strategy [mixing different packs, coupons, etc]. The highest profit submission will receive a letter grade boost. {2 marks]