BamBam and Gunnar are brothers who like to setoff fireworks

Bam-Bam and Gunnar are brothers who like to set-off fireworks that their mom buys for them. Bam-Bam likes them more than Gunnar, so suppose their utility functions for fireworks are given by: UB = 2 × ln ( fB +1) and UG = ln ( fG +1). Suppose further that their mom is willing to buy only a total of 10 fireworks (i.e., her sons is given by SW = UB +UG fB + fG = 10 ), and suppose that her social welfare function for because she “loves them equally.” Use calculus to determine the allocation of fireworks that maximizes social welfare (your answer may not involve whole numbers) and verify your answer with a spreadsheet graph of the possible values for social welfare. Now suppose Gunnar gets startled each time Bam-Bam sets-off a firework. Suppose Gunnar’s utility function is now given by: UG = ln ( fG +1) - fB . Use calculus to determine the optimal allocation of fireworks (your answer may not involve whole numbers) and verify your answer with a graph.

Solution

In this case study has more utility in fireworks in comparison of Gunnar so their mother gives more no of fireworks then Gunnar.

The final distribution of goods and services must be equitable (i.e., fair). If the form of economic organization is competitive markets, this also requires the initial distribution of resources be equitable.

Equity is a normative concept, with no universal definition; what is equitable to you is equitable to you, but not necessarily equitable to me, and what is equitable to me is equitable to me, but not necessarily equitable to you. Note that an equitable distribution is not necessarily an equal distribution.

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.