Question [1]: Consider a consumer with endowment vector (4, 6). For each of the following utility functions, draw representations of the consumer's Engel curves, Income Expansion Path, Demand Curves, and a Price Offer curve. When drawing the Price Offer curve, assume the consumer has some endowment vector with strictly positive quantities of both goods. 1. (Cobb Douglas) u(x) = Ir, "; a E (0, 1). 2. (Leontief) u(x) = min{ari, x2}, a > 0. 3. (quasi-linear) u(x) = r, + 10lnrg 4. (perfect substitute) u(r) = ar + 12; a >0 5. u(x) = min($1, VI2} 6. u(r) = max {ari, 12}, a >0