Question

5. Draw out examples of each of the following indifference curves: imperfect substitutes, perfect substitutes, and perfect complements.

6. Jody enjoys having exactly 1 teaspoon of sugar with every cup of coffee she has. What does this say about her indifference curves between the two goods? What happens to her utility level when she is given 5 teaspoons of sugar with one coffee? (Just an explanation)

7. Jay’s Utility function is given by U(x,z) = 3x₁^0.2 x₂^0.8 and P₁=$2 and P₂=$4 and his budget is $200.

• Write out the Lagrange but don’t solve it
• Find the utility maximizing values of x₁and ^Â x₂

8. What does the substitution effect cause a consumer to do if the price of a good increases?

9. What does the income effect cause a consumer to do if the price of a good increases? What else is needed here?

10. What can we say about the substitution and income effects on a decrease in wages? What is an Engel curve and how does it relate here? If leisure is viewed as an inferior good, how would the labor demand curve look?

11. Suppose m=120, p1= 5, and p2=6.

• What is the budget equation?
• What is the slope of the budget line?
• How does the budget set change with the following:
  • a 20% increase in m
  • a 2$ decrease in p2

Answer 1

5.

Imperfect substitutes: Utility functions for these preferences will be quasi linear. Example: $\dpi{80} \fn_phv \small u(x,y)=\sqrt{x}+y$

10 15 20

Perfect substitutes: Utility functions for these preferences have a constant MRS. Example: $\dpi{80} \fn_phv \small u(x,y)=2x+y$

Perfect complements: Consumers consume complements in a fixed ratio. Example of a utility function: $\dpi{80} \fn_phv \small u(x,y)=min(2x,3y)$

6. The consumer treats one teaspoon of sugar and one cup of coffee as perfect complements and would consume the two goods in exactly this ratio. Increasing the quantity of one of the goods will not give the consumer any additional utility. The consumer's preferences can be represented by the following utility function: $\dpi{80} \fn_phv \small u(x,y)=min(x,y)$ .

The indifference curves are L shaped.

If the consumer is given 5 teaspoons of sugar with one cup of coffee, her utility will be the same as the original bundle of one teaspoon of sugar and one cup of coffee (1).