Consider the following social welfare function for a small community of five people.

Place positive and negative signs above all the terms in the function, illustrating whether

they increase or decrease each person's utility.

Assume that producing all types of goods $($both $N$ and $C)$ requires some level of pollution.

Will an increase in the consumption of non$-$competitive goods always increase social

welfare?

Now, let $C_b$ be a new mansion on Cape Cod. Let $P$ be the environmental costs of building the

mansion. Finally, let $C_a{C}_c,C_d$ and $C_e$ be the status impact on folks who are not Ms$.b$ arising from

the new mansion. Assume that the positive increment to individual utility for Ms$.b$ of a one$-$unit

increase in $C_b$ equals $$10,000$ in consumer surplus and that the negative status increment to other

people is $-$ $$2,000.$ Assume also that a one$-$unit increase in $C_b$ produces one unit of $P,$ which

decreases everyone's consumer surplus by $$500.$

What are the private benefits to Ms$.b$ of consuming one more unit of $C_b?$

What are the environmental costs to Ms$.b$ consuming one more unit of $C_b?$

What are the status costs to others to Ms$.b$ consuming one more unit of $C_b?$

Will social welfare increase if Ms$.b$ builds her mansion?