When answering these questions, answer as if you were answering a short-answer question. The math is used as if it were part of the sentence.

1. Your income is m. You consume two goods: x and y. Your utility function is given by u(x, y) = x ² y.

(a) Using given prices p_x and p_y, solve for your optimal choice of x and y.

(b) Explain in a couple lines describing what these demand functions say about how you choose your optimal consumption of x and y.

2. We want to think about Andrea's entire budget, so we break her budget into two segments: consumption (c) and saving (s). The utility function is u(c, s) = c + s.

(a) How does a person get utility from saving?

(b) Using the prices p_c and p_s, what is Andrea's budget constraint and solve for the rate at which the market is willing to substitute saving for sending. Explain what this rate represents in reality.

(c) Solve for Andrea's optimal choices of consumption and saving given her budget constraint.

3. Consider the policy problem of deciding whether to increase the fare for taxi) in Barbados. Ignoring everything else, consider how this would affect the taxi's behavior. Taxis behave badly on the road, often committing multiple traffic violations each day. They receive a fare of f for each passenger. Being sure to justify all your answers, consider the following questions:

(a) Write the taxi's optimization problem by considering first what they get utility from, what they get disutility from, and whether they face any constraints. (Hint: recall probabilities -they might be useful here).

(b) If the aim of the policy is to improve behavior, what would your recommendation be? Increase bus fare or reduce it?

4. Consider an individual with the utility function u(x1, x2, x3) = x ₁ x ₂ x ₃ . Solve for this individual's demand functions, and discuss how these goods are related through their marginal utilities.