Problem
Pam Shea has preferences represented by the utility function u(a, b) = ab 100 , where a is the number of ounces of animal crackers that she consumes, and b is the number of ounces of beans that she consumes.
1. On a graph, sketch the locus of points that Pam finds indifferent to having 8 ounces of animal crackers and 2 ounces of beans. Also sketch the locus of points that she finds indifferent to having 6 ounces of animal crackers and 4 ounces of beans.
2. Jessica Christian has preferences represented by the utility function v(a, b) = 1000a 2 b 2 , where a is the number of ounces of animal crackers that she consumes, and b is the number of ounces of beans that she consumes. On another graph, sketch the locus of points that Jessica finds indifferent to having 8 ounces of animal crackers and 2 ounces of beans. Also sketch the locus of points that she finds indifferent to having 6 ounces of animal crackers and 4 ounces of beans.
3. Are Pam's preferences convex? Are Jessica's preferences convex? Explain.