Crystal$$s utility function is given by U$($B$,$C$)=$B$*$C$,$ where B is the number of burgers per

week and C is the number of packs of cigarettes per week. Thus, MUB$=$C and MUC$=$B$.$

a$.$ What is the equation for the marginal rate of substitution?

b$.$ If her income is $$240$ per week, and prices are PB$=8$ and PC$=4,$ how many burgers and

packs of cigarettes does she purchase to maximize her utility?

c$.$ The government wants to cut down the consumption of one these items $...$ so it taxes

burgers, which increases PB to $$12.$ Now what are the optimal choices of B and C for

Crystal?

d$.$ On the same graph, illustrate your answers to parts $($b$)$ and $($c$)$