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 from Page 1 of 3 ZARIDIS I of Business & Economics the days before pogs became the global currency). Although they are unable to produce any goods, they are very fortunate and each of them 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 2 jars 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) = poz and Silvio's utility function is U(p. c) = 3pc . a. [4] Characterize the set of Pareto Optimal allocations of peanut butter and cleanCoins across Humza and Silvio. Suppose that the lone Cryptocon 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. [6] Find the equilibrium price of cleanCoin (p ) 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