1. Your income is m. You consume two goods: I and y. Your utility function is given by U(I, y) = ry. (a) Using given prices p, and py, solve for your optimal choice of z and y. (b) Write a couple lines describing what these demand functions say about how you choose your optimal consumption of r and y. 2. We want to think about Andrea's entire budget, so we break her budget into two seg- ments: consumption (c) and saving (s). The utility function is u(c, s) = Box | s. (a) How does a person get utility from saving? (b) Using the prices pe and pa, write 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 ZRs (route taxis) in Barbados. Ignoring everything else, consider how this would affect the ZR's behaviour. ZRs 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 ZR's optimisation problem by considering first what they get utility from, what they get disutility from, and whether they face any constraints. (Hint: recall probabilities from ECON1005-they might be useful here). (b) If the aim of the policy is to improve behaviour, what would your recommendation be? Increase bus fare or reduce it? 4. (To be solved on your oum. ) Consider an individual with the utility function u($1, 12, 13) = In1213. Solve for this individual's demand functions, and discuss how these goods are related through their marginal utilities