Assume there are only two consumers - Ellen and Mattie - in a market for a good. Ellen has the following demand function: ????(??,????, ????,??) = 6 ???+ 2 ??????2 ????? + ?? 100 Mattie on the other hand, has the following demand: ????(??,????,????,??) = 2 ?2??+ 6?????2???? + 2?? 100 Assume both Ellen and Mattie have the same income (??= 1,000 for both). In addition, they are both price takers and face the same prices (???? = 1,???? = 4). a. Solve for the aggregate quantity demanded as a function of the price (??). b. Suppose the aggregate supply function for the good is given by ????(??) = 5 + 2??. What will be the equilibrium price (????) and quantity (????)? c. At the equilibrium price, how much will Ellen purchase and how much will Mattie purchase? (Note: make sure the sum of their individual levels of consumption add up to the aggregate quantity produced and consumed in the equilibrium outcome solved for in part (b).) 2. Assume the aggregate demand and supply for a good are given by the following expressions: ????(??) = ?1 2??(25 ???) and ????(??) = 2 ????10 a. Solve for the competitive equilibrium price (????) and quantity (????). b. At the competitive equilibrium, what is the elasticity of demand (??)? c. At the competitive equilibrium, what is the elasticity of supply (??)? d. Suppose the government imposes a per-unit tax of ?? = 5 on each unit of the good produced. What would be the resulting equilibrium quantity? What price would consumers pay (??????????) and what price would sellers receive (??????????)? e. Which group (producers or consumers) paid a larger share of the tax? (That is, which impact was more pronounced, the increase in the price consumers pay or the decrease in the price sellers receive?)