3. [20] It is the year 2050. Humza and his friend Silvio Bartolo Fernandez (SBF) are the only two attendees of Cryptocon (a crypto industry conference that is a legacy event fromthe days before pogs became the global currency). Although they are unable to produce any goods, they are very fortunate and each ofthem has an endowment of peanut butter {denoted p] and cleanCoin (denoted c), a cryptocurrency that is associated with the initial coin offering a dietary cleanse. Humza has 3 jars of peanut butter and 2 cleanCoins, while SBF has Zjars of peanut butter and 4 cleanCoins. Although they both enjoy the products, they have different preferences over them; Humza's utility function is U(p, c) = put:2 and Silvio's utility function is U(p, c) = 31):: . a. [4] Characterize the set of Pareto Optimal allocations of peanut butter and cleanCoins across Humza and Silvio. Suppose that the lone lCryptocon attendees decide to engage in trade. b. [4] Normalizing the price of peanut butter, find their demand functions for cleanCoin. c. [2] Write the excess demand function for cleanCoin. d. [5] Find the equilibrium price of cleanCoin (pg) that clears the two markets. How many cleanCoins and how much peanut butter does each of them consume in the competitive equilibrium? e. [4] Is the competitive allocation that you found in part {d} the only Pareto Optimal allocation that Humza and Silvio could reach through voluntary exchange, given their initial endowment? Explain. [6] Robinson Crusoe has exactly 15 hours per day to spend gathering coconuts or catching sh. He can catch 4 fish per hour or he can pick 12 coconuts per hour. His utility function is U(F, C) = FC where F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best possible way between catching sh and picking coconuts, his consumption will be the same as it would be if he could buy sh and coconuts in a competitive market where the price of coconuts is 51. What is the price of sh and what is his income [at competitive equilibrium prices}