Forum de mathématiques - Bibm@th.net

To prepare for better prospects in the job market, you decide to focus more on Soft Skills for the
3 remaining years that you will spend at your business school. In the following, you will use
Consumer Theory to analyze your optimal strategy to maximize your average grade/level in Soft
Skills (denoted x) as compared to your average grade in Hard Skills (denoted y). Assume that
grading Soft Skills does in fact exist although these skills are difficult to quantify.
Let’s denote by Tx the time in years that you devote to Soft Skills and by Ty the time in years that
you devote to Hard Skills.
1- Write your time constraint.
2- Although you care more about Soft Skills, you are better at Hard Skills. Assume that your
productivity in Soft Skills is 2 average-grade points per year of study and that your
productivity in Hard Skills is 3 average-grade points per year of study. Find your
production constraints: the relation between x and Tx, the relation between y and Ty.
3- Then derive the final constraint that you are facing in terms of x and y only.
Suppose your utility function over x and y is given by
U(x,y)=2 log(x) + log(y), where x>0 and y>0.
4- Demonstrate that U(.,.) is a relevant utility function and interpret in words each
mathematical relation. Check that the diminishing marginal utility property is verified.
5- What are the indifference curves in this context? What is the meaning of downward sloping
curves? Should higher indifference curves be preferred to lower ones? Should these curves
be bowed inward?
6- Derive numerically your optimal bundle (x, y) and your optimal (Tx, Ty). Interpret your
result.