Households derive utility from the consumption of apples (a), bananas (b), and coconuts (c). The consumption of apples and bananas is taxed at rates 7 and 7, respectively. Each household can supply up to L hours of labor at an hourly wage of w. Households solve Mar a,b,cl 1- Ta IL + s.t. Pa(1+Ta)a+po(1+7)b+c=lw where a > 0 and 7 > 0. The three commodities are produced using constant-productivity technologies in labor. An hour of labor produces , apples when employed in the production of apples, z, bananas when employed in the production of bananas, and ze coconuts when employed in the production of coconuts. There is free labor mobility across sectors (wages are equalized), firms are atomistic and price takers, and firms' problems are described as Max (Pazala-wla} la Max (pls-wl} 16 Max {zele-wle} The productivity levels take the values za = 2. 2=5, and ze = 1.5. The preference parameters take the values a = 0.25 and 7 = 1.5. The maximum number of hours households can work is normalized to L = 1. i) What is the equilibrium consumption of apples, bananas, and coconuts when tax rates are zero. You can use coconuts as the numeraire. What are the demand elasticities for apples and bananas in that equilibrium? ii) Now assume the government needs to raise tax revenues equivalent to 0.06565 units of coconuts. The government can only tax the consumption of apples and bananas. The government is benevolent and chooses its taxes to maximize aggregate welfare, which includes the welfare of consumers, firms, and the government itself. What are the optimal taxes on apples (Ta) and bananas (7)? You need to solve for a non-linear equation to find them numerically. For example, you can use the function fzero in Matlab. What explains the difference in tax rates, if you find any difference? iii) How much does consumption of apples and bananas change with the tax scheme found in ii)? Interpret your findings. iv) What would be the optimal taxes if the government needed to raise 0.1294 in tax revenues? Interpret the difference with the answer found in ii).