Consider an economy with two types of consumers, which differ in their endowments: type-1 people own 10 units of good x and none of good y, while type-2 people own none of good x and 10 units of good y. Both types of consumers like to consume both goods, with the same preferences over consumption bundles (i.e. the same utility function). For each of the following utility functions, do the following: a. Find the market equilibrium price ratio and optimal consumption bundles when there are 100 individuals of each type. b. Find the market equilibrium price ratio and optimal consumption bundles assuming now that there are 100 individuals of type-1, but only 50 of type-2. Tip: You will need a numerical solver (such as Wolfram Alpha or MATLAB) to do the extra credit question. Common homothetic utility functions 1 2 xiy 1. Cobb-Douglas: U(x, y) = 2. Constant Elasticity of Substitution (CES):U(x, y) = | xi + ) yi Non-homothetic utility function 3. Quasilinear: U(x, y) = x + log(y) 4. EXTRA CREDIT: U(x,y) = (;)x