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Questions tagged [perfect-substitutes]

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Competitive equilibrium in a two-person economy with substitutes and complements

Recently came across this question on a microeconomics test and there was something that did not sit quite right with me. In an economy with two agents, A and B, and two goods, milk and honey, the ...
Jovan Jezdic's user avatar
0 votes
0 answers
38 views

How can I determine the potential nature of goods in an economy, given that they are perfect substitute?

Question: There are a total of 5 different goods produced and consumed in the economy. Two of these goods, X and Y, are perfect substitutes. Which of the following statements are true? X can be a ...
ZZZ's user avatar
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1 vote
1 answer
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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 ...
Polario's user avatar
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1 vote
1 answer
873 views

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 ...
Nicolas Torres's user avatar
2 votes
2 answers
261 views

Finding Walrasian equilibria when Walrasian demands are not unique

I'm trying to solve the following excercise: Find the Walrasian equilibria for a pure exchange economy where agents' ($A$ and $B$) preferences and endowments are given by: $u_A = x_A + y_A$ $u_B = 2 ...
Nicolas Torres's user avatar
5 votes
1 answer
1k views

How to find the contract curve when both agents have linear utilities?

I'm trying to solve the following excercise: Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by: $u_A = x_A + y_A$ $u_B = s x_A + y_A$ $...
Nicolas Torres's user avatar
2 votes
0 answers
64 views

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 ...
Athaeneus's user avatar
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3 votes
1 answer
581 views

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 ...
Sceptical_Economist's user avatar
1 vote
0 answers
67 views

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 ...
not tdm's twin's user avatar
1 vote
1 answer
100 views

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 ...
Leo Simon's user avatar
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1 vote
1 answer
261 views

Contradictory FOC and maximizing solution

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 ...
Elina Gilbert's user avatar
5 votes
1 answer
2k views

Perfect substitutes and Lagrange

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,...
Jesper Hybel's user avatar
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