Consider an economy that is similar to the one in question 4. Suppose I = 3 people live in this economy and each agent has a productivity wi = 2i. Suppose further that an agent who consumes c units of consumption and earns y units of income has preferences y y2 u(c, w ) = c ? 2w2 . Suppose government uses affine income tax system T (y) = ty ? d. Define Y = PIi=1 yi as aggregate income in the economy. a. Define an equilibrium with affine taxes. b. Solve worker i’s problem to calculate yi as function of (1 ? t). What is the elasticity of yi with respect to (1 ? t)? c. Calculate laissez-faire equilibrium Y , and top-to-middle and middle-to-bottom con- sumption ratios, c3 and c2 . c2 c1 d. Calculate d in equilibrium when when t = 25%. Calculate also Y , and c3 and c2 . c2 c1 e. Compare the equilibrium allocation under t = 25% to the laissez-faire equilibrium allocation in terms of aggregate income and consumption inequality ratios. Is there an equality-efficiency tradeoff?