Total differential, level curve. (please check work)

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SUMMARY

The discussion focuses on the total differential and marginal rate of substitution (MRS) for the function u(x1, x2) = ax1 + bx2. The total differential is calculated as du = adx1 + bdx2, where fx1 = a and fx2 = b. The MRS is derived from the equation adx1 + bdx2 = 0, resulting in MRS = a/b. The mathematical approach is confirmed as correct, despite the contributor's lack of economics knowledge.

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Homework Statement



For u(x1, x2) = ax1 + bx2

a) find total differential
b) Draw a representative level curve for u = ubar (u with a line over it)
c) Find MRS (marginal rate of substitution)


Homework Equations



u(x1, x2) = ax1 + bx2


The Attempt at a Solution


a)
fx1 = a
fx2 = b
du = fx1dx1 + fx2dx2
du = adx1 + bdx2

b)
Без імені.jpg


c) adx1 + bdx2 = 0
bdx2 = -adx1
-(dx2/dx1) = a/b

∴ MRS = a/b
 
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I don't know economics. But mathematically, your answers look good to me. (I looked up the definition for marginal rate of substitution, and that suggests you have the right answer).
 
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BruceW said:
I don't know economics. But mathematically, your answers look good to me. (I looked up the definition for marginal rate of substitution, and that suggests you have the right answer).

Yes, I should've added something about that. Thanks :-).
 

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