Questions on Constrained Optimization, Derivative of Demand & Cost Minimization

1. Alex Ovechkin's utility functiOn for hockey helmets (h) and spare teeth (15) is U(h, t) = x/f_L(t 1). The prices are ph = 4 and pt = 6 while Alex's income is 42. Find his optimal consumption bundle. Alex Ovechkin's utility function for hockey helmets (h) and spare teeth (t) is U(h, t) = ln(ht) + 1n h. The prices are pk = 4 and pt = 8 while Alex's income is 48. Find his optimal consumption bundle. 2. Consumer's utility is U (331, 3:2) = min(a:1 + 1, 22:2). Prices are 101 and p2, income is I. Derive the demand function for 3:2. Consumer's utility is U (3:1, 3:2) = 23:1 + 33:2. Prices are p1 and 1312, income is I. Derive the demand function for 331. 3. Consumer's utility is U (331, 132) = 1131 +2332. Derive the expenditure function E (191, 102, U) Consumer's utility is U (:61, $2) = min(:c1, 2:62). Derive the expenditure function E (pl, 132, U). 4. Consumer's utility is U(:1:1, $2) = :31 + 1n 3:2. You know that the optimal bundle is 331 = 0, 332 = 5. What can you say about 191,102 and I? Consumer's utility is U (:31, 2:2) = ln(x1) + $2. You know that the optimal bundle is 3:1 = 10, 11:2 = 0. What can you say about 101,192 and