Microeconomics Question

Question

4 goods = a,b,c,d

wealth =12

pa=1

pb=1

pc=2

pd=2

thus constraint is a+b+2c+2d=12

maximise u = ab+cd

subject to constraint

Answer 1

MU(a)=b MU(b) =a MU(c) =d MU(d) = c

We Need MU(a)/MU(b) = pa/pb MU(a)/MU(c) = pa/pc MU(a)/MU(d) = pa/pd etc

MRS (ab)= b/a MRS (ac) b/d MRS (ad) b/c.

note pa/pb=1 pa/pc = pa/pd = pb/pc =pb/pd =1/2.

Tangency has b/a =1 or b=a b/c=b/d =1/2 or 2b =c=d

We substitute into the budget constraint

12 = a+b +2c +2d = b + b +2*2b +2*2b or 10b=12 so b = 12/10 a= b =12/10

c and d both = 2b or 2.4

formally,,

a* = 1.2

b*=1.2

c* = 2.4

d* = 2.4