# Questions tagged [perfect-substitutes]

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### Income effect in perfect substitutes if the already cheaper good becomes more cheaper?

Consider a simple utility function U(x,y) = x+y such that Px < Py (which means only x is being consumed at optimal point, a corner solution). In this case, assume Px falls further. Now won't the ...
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### How to find the contract curve for a funky utility involving the min operator?

Suppose a pure exchange economy where agents’ ($A$ and $B$) preferences are given by the following utility functions: $u_A = \min(3x+y,x+3y)$ $u_B = x^\frac{1}{2} y^\frac{1}{2}$ Find the contract ...
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### Relation between complements and substitutes (for multiple goods)

I am a little bit curious about the following problem: If we have multiple goods (at least 3 or more)... And we know that $x_1$ and $x_2$ are substitutes and $x_1$ and $x_3$ are also substitutes, does ...
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### A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes

So the most prominent preferences are perfect substitutes, perfect complements and cobb-douglas preferences. Perfect complements and perfect substitutes are extreme cases and I was asked whether there ...
1 vote
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### Perfect substitutes mathematical definitions not equivalent

Statement: Consider goods $X$ and $Y$ (and we denote the quantities of by the same notation) such that they are perfect substitutes with the substitution ratio $1:n$. Assume the basic axioms ...
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### Example of a (not quasi-linear) production function whose inputs are not perfect substitutes but are not asymptotic at the axes

I'm looking for an example of a family of production functions indexed by, say, rho, where the inputs become closer and closer to perfect substitutes as rho approaches 1, and yet, the marginal product ...
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I have to maximize the following function - $\max_{x \in (0,1)} (((p_1x)^{2r} + (p_2(1-x))^{2r})/2)^{1/r}$ where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered to be ...
How does one solve utility maximization of perfect substitutes using Lagrangian function? Consider the problem $$\max_{x,y} ax +by$$ subject to the constraint that $$px + qy \leq I$$ where \$a,b,p,q,...