optimal consumption question?

U = C1 + A•(C1)^w • (C2)^z + C2

Since interest=0 then there aren't any discounting process, so Income=∑C

∑C=C1+C2

Or

C=C1+C2

C1=C-C2

C is constant

substitute:

U = C1 + A•(C1)^w • (C2)^z + C2 = (C-C2)+A•(C-C2)^w • (C2)^z + C2

then expand:

U = C - C2 + A • (C-C2)^w • (C2)^z + C2

U→MAX if ∂U/∂Y=0 (FOC, skipping SOC)

∂U/∂Y = -A•w•(C-C2)^(w-1)•(C2)^z + A•(C-C2)^w •(C2)^(z-1) = 0

Solving equation:

A•w•(C-C2)^(w-1)•(C2)^z = A•(C-C2)^w •(C2)^(z-1)

will yield utility-maximizing intertemporal consumption transmission rule:

C2 = C•z/(w+z)

C1 = C-C2 = C(1 - z/(w+z)) = C•w/(w+z)

Answ:

C2=C•z/(w+z)

C1=C•w/(w+z)

the respond is D. because of the fact the above answerer pronounced, the biggest equation to evaluate is MUx/MUy = Px/Py. that's the mandatory difficulty for optimal intake. in spite of the undeniable fact that, this difficulty does not in any respect require that MUx/MUy = a million. in specific cases you are going to have products that do in simple terms not provide you as plenty excitement as others, and, greater importantly, each thing does not cost a similar. If Px does not equivalent Py, then Px/Py isn't a million. it shouldn't stop the buyer from looking an optimal answer. to furnish you an occasion, enable's fake X replaced into vehicles and Y replaced into apples. the charges of those products are going to be ridiculously far aside--according to danger $15000 for the vehicle and $a million for the apple. in case you're making an optimal intake selection you shouldn't be searching for the factor the place MUx/MUy is a million; as according to the equation, MUx/MUy could desire to be 15000. So if we've been in the situation above, looking the optimal intake kit could correspond to selection A. that's truthfully a possibility. in addition, if X have been greater low cost than Y, you're able to land up describing selection B. If this does not make plenty sense, look at this type. in case you carry out extremely of algebra (specifically, multiplying the two facets by ability of MUy and then dividing the two by ability of Px) to rewrite the equation as MUx/Px = MUy/Py, you may truthfully get the two area to intend some thing. MUx/Px ability marginal application of the stable according to dollar I ought to spend to get it, that's a complicated way of asserting "bang for my dollar while i'm procuring stable X". So, going to back to the vehicle occasion till now, if we are saying MUx/Px = MUy/Py is the mandatory difficulty, what we are fairly asserting is that we want the bang for the dollar for vehicles to be a similar because of the fact the bang for the dollar of apples. If i bypass to be spending $15000 on a automobile, i could greater powerful be getting a minimum of as plenty leisure from it as i could from 15000 apples. that's form of a humorous way of putting issues, in spite of the undeniable fact that it could assist you hit upon slightly greater attitude.