Consider the utility function u(x1; x2) = x1^(1/2)x2^(1/2) . Let the prices of good 1 and good 2 be p1 and p2, and of course let the consumer’s…

Consider the utility function u(x1; x2) = x1^(1/2)x2^(1/2) . Let the prices of good 1 and good 2 be p1 and p2, and of course let the consumer’s income be m.
1) State the consumer’s maximization problem and use this problem to derive his demand functions for the two goods.
2) Is good 1 ordinary or Giffen? Is good 1 normal or inferior? Is good 1 luxury or necessary? How can i explain this?
3) Suppose the prices per unit for the two goods are p1 = p2 = \$2 and the consumer’s income is m = \$100. How can I calculate his optimal consumption bundle?
4) Now suppose the price of good 1 increases to p’1 = \$4 per unit. What is his new optimal consumption bundle?
5) Calculate the substitution effect and the income effect of the price change in demand of good 1. How can I illustrate them on a graph?

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