1. (a) What is the conceptual difference between a choice based on the maximization of a single objective versus a choice based on maximization with two or more objectives. Illustrate the difference by making up a specific example where a decision maker is making a choice (i) with multiple objectives, (ii) with a single objective.
(b) Finally, suppose there are two potential objectives, but this particular decision maker cares only about one of those objectives and not at all about the other. Draw a diagram with the amounts of each objective on the axes, and then show what his indifference curves look like.
2(a) How does a corner solution to the consumer's utility maximization problem differ from a standard, interior solution?
(b) Describe some types of preferences that can lead to a corner solution. What is the shape of the indifference curves? What happens to the marginal rate of substitution in those cases?
(c) A consumer is at a corner solution - he buys meat, eggs, and vegetables, but no fish. The price of fish rises. Will this change his consumption of fish? The price of fish falls. Will this change his consumption of fish? In each case, draw an appropriate diagram to illustrate your answer
3. The Stone-Geary utility function is derived from, but different than, the Cobb-Douglas utility function. In what key way do Stone-Geary preferences differ from Cobb-Douglas preferences? If you could observe the demand functions of a consumer, how does the demand function differ if the consumer had Stone-Geary preferences versus Cobb-Douglas preferences?
4. (a) Write down the equation for a demand function for coffee giving the quantity of orange juice consumed per month (x) as a function of the price of orange juice (po), the price of milk (pm) and household income (y), where the own-price elasticity of demand for orange juice, the cross-price elasticity of demand with respect to the price of milk, and the income elasticity of demand are each constant (i.e., do not vary at different levels of price, income or consumption). (b) Suppose the own-price elasticity of demand varies with the number of children in the household (z) - the more children, the lower the price elasticity of demand. Modify the equation you provided in (a) to accommodate this.