SUMMARY
The discussion focuses on the total differential and marginal rate of substitution (MRS) for the function u(x1, x2) = ax1 + bx2. The total differential is calculated as du = adx1 + bdx2, where fx1 = a and fx2 = b. The MRS is derived from the equation adx1 + bdx2 = 0, resulting in MRS = a/b. The mathematical approach is confirmed as correct, despite the contributor's lack of economics knowledge.
PREREQUISITES
- Understanding of total differentials in calculus
- Familiarity with the concept of level curves
- Knowledge of marginal rate of substitution in economics
- Basic algebraic manipulation skills
NEXT STEPS
- Study the implications of total differentials in multivariable calculus
- Explore graphical representations of level curves for various functions
- Research the economic significance of marginal rate of substitution
- Learn about optimization techniques in economics
USEFUL FOR
Students in calculus and economics, particularly those studying multivariable functions and their applications in economic theory.