extra problem set 4 (#1)
i have spent way to much time on this question,but here we go:
Charlie’s utility function is xAxB. The price of apples used to be $1, the price of bananas used
to be $2, and his income used to be $40. If the price of apples increased to $5 and the price
of bananas stayed constant, the substitution effect on Charlie’s apple consumption would
reduce his consumption by (choose the closest answer)
so what i got for point A (20,10)
demand for xa=m/2pa
and xb=m/2p2
xb may be irrelevant by how the question only asks for a change in apples
point b: plug in 20 and 10 into the util function of u (XaXb)=200 utils
finding our ibc
- since we know this is a cobb douglas equation by how it does have dmrs(its on my notes and im lazy to write it right now)
-so we use our previous demands from point A and we multiply them
-xa=m/2pa
-xb=m/2p2
when we multiply the demands we get (m-squared/2pa times 2pb)
so its (m squared/40=200utils)
then we multiply 40 by both sides to get m squared=1600(i multiplied by 14 like an idiot, dont do this, multiply by 40)now its 8000 utils,( radical both sides to get our ibc of 89.44)
wow, i just realized what i did wrong and i dont feel like wasting what i put up sooo:
might as well help some fellow gauchos.
using the apple demand, xa=m/2pa(dont forget the new price of 5)
we get 89.44/10=9, but 11 is the closest...it is C.