please find the answer for the following question

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Consider the following utility functions. Do this homework for all the functions below, but only submit your answers for the functions in parts b, c and g. a. U(x1, 12) = xx b. U(X1, 2) = raz-a c. U(x1, X2) = (x1 + a) 3(x2+6)3 d. U($ 1, 12) = (x1 + a) " (x2 + 6) 1-a e. U(x1, 12) = Inc1 + 22 f. U(x1, 262) = f(21) + 12 g. U(X1, 12) = 23+32 h. U(x1, 12) = x7 + 29 1. For each of the utility functions above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are p1 and p2, and the consumer has an income m. 2. For each of the utility functions above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are p, and p2, and the consumer has an endowment (e1, e2) of the two goods. 3. For each of your answers in question 2. above, write down the consumers net demands for the two goods at prices p1 and p2. Find the ratio of prices 21 for which the net demand for good 1 is zero. Also find the price ratio at which the net demand for good 2 is zero. 4. Can you explain your answer to question 3. above intuitively