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Consumer with utility function

Assignment: Consider a consumer with utility function u(x_{1},x_{2}) = x_{1}^{0.5} x_{2}^{0.5}

Problem 1: Find the demand for any vector of strictly positive prices, p = (p_{1},p_{2})>>0 and any level of income, M>0,. Why does the consumer end up spending her entire income (i.e., choose a consumption point on the budget line)?

Problem 2: Sketch some indifference curves of the utility function u and draw the price consumption curve (PCC), which results when varying the price of the first good. Does the first good have a normal price effect, and how does this show in the PCC?

Problem 3: Is the following statement true or false: A normal good (a good with positive income effect) cannot be a Giffen good. Explain briefly why you arrive at your conclusion.

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## Q : Market equilibrium and profit maximization

The supply and demand equations for a hypothetical perfectly competitive market are given by QS = -100 + 3P and QD = 500 - 2P. A) Find the market equilibrium price algebraically.