1 Consider the utility function: U(X,Y) = 10XY a. Show that this function satisfies the assumption of non-satiation. b. What is the equation of an indifference curve of this function at utility U = 100? c. Find an expression for the slope of the indifference curve. Show that the indifference curve of this function is downward sloping. d. What is the MRS? How does the absolute value of the slope of the indifference curve change when X increases? Problem 2 Remember that in our discussion in class, we said that when preferences satisfy the three axioms of rational choice (completeness, transitivity and continuity), we can derive a full ranking of all outcomes according to the preference. We extended that result to mean that we could represent the ranking mathematically using a utility function, but that there isn't just a single representation that would be valid. Rather all utility functions that preserve the ranking of the outcomes according to the preference would be valid. Of the options below, which two utility functions could represent the same underlying preference? a. U (x1 x2)=x1 + x2 b. U (x1 x2) (x1+x2)2 c. U (x1; x2)=x12x2 d. U (x1,x2)=x1x2 Problem 3 V (x1 x2) 2x1 + x2 V (x1; x2) = 2x1x2 V (x1; x2) x1 + x2 V (x1;x2) = (x1x2)0.5 The following combinations of goods X and Y represent various market baskets. Consumption is measured in pounds per month. Units of good Units of Market basket good Y A 4 6 B 16 7 C 15 3 D 3 2