Question

Bridget has a limited income and consumes only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle, and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget's utility, while the last pound of cheese added 40 units. Is Bridget making the utility-maximizing choice? Why or why not? If not, what should she do instead? Why?

Answer 1

Cost = 10 w + 4 c
d (cost) = 10 dw + 4 dc
d (utility )= 50 dw + 40 dc

her present state is
w = 4
c = 10

Cost = 40 + 40 = 80
to stay at the present cost
10 dw + 4 dc = 0
or
dc = - (2.5)dw
so
d Utility at present cost = 50 dw -40(2.5) dw
= 50 dw - 100 dw = -50 dw

so if I increase wine by 1, I decrease cheese by 2.5
AND I decrease my utility by 50!!!
eat more cheese, less wine !!!