5 votes

Perfect complement preferences in an exchange economy

Set of Pareto Efficient Allocations consists of feasible allocations $((x_J, y_J), (x_D, y_D))$ satisfying $y_J=\displaystyle\frac{x_J}{2}$. Competitive Equilibrium is the price $(p_x, p_y=1)$ ...
Amit's user avatar
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3 votes
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What is the reason behind the demand function of a perfect complement good?

Suppose you have $M=20$ to spend on shoes. Left shoes cost $p_L=5$ and right shoes cost $p_R=5$. A bundle, $(x_L,x_R)$ consists of $x_L$ pairs of left shoes and $x_R$ pairs of right shoes. How would ...
Ubiquitous's user avatar
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3 votes

Doubt regarding Walrasian equilibrium with complements for both agents

Since demand equals supply holds for every price $p$, this simply means that every $p$ is an equilibrium price. However, the equilibrium allocation that $p$ supports varies with $p$. To be precise, ...
Amit's user avatar
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3 votes
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Can a complement good be free or have a fixed cost?

Air is a complement good for a lot of things. If you get no air at all then food, gold and iPhones give you no utility either. And air is free! Except in Spaceballs...
Giskard's user avatar
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2 votes

Can a complement good be free or have a fixed cost?

Public goods are goods which have a fixed cost and are sometimes free for businesses. Think of police. They patrol streets, protecting businesses premises. Businesses do not pay directly for these ...
Robert_T's user avatar
2 votes
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Optimal consumtion bundle of lemons and sugar

Alex's preferences of sugar and lemons can be expressed in form of a utility function as: $U(x,y)=min(x/2,y) $ where $x$ is sugar and $y$ is lemons.This function tells us we need at least 2 spoons ...
EconJohn's user avatar
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2 votes

Perfect Complements - Walrasian Equilibrium

If the prices $p_1$ and $p_2$ are positive than as you pointed out the equations \begin{eqnarray*} \frac{30p_1}{p_1+p_2} + \frac{20p_2}{p_1+4p_2} & = & 30 \\ \\ \frac{30p_1}{p_1+p_2} + ...
Giskard's user avatar
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2 votes

Relationship between convexity and a perfect complements type utility function

$u(x, y) = -\max(x, y) = \min(-x, -y)$ is a concave function. Since it is concave, it is also quasiconcave (or equivalently, it represents weakly convex preferences). Here is the indifference map of $...
Amit's user avatar
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2 votes

Relationship between convexity and a perfect complements type utility function

Instead of directly giving you the answers, I'm going to give you a series of hints to help you figure out the answers on your own. 1.What would be the shape of the indifference curve? Consider ...
Herr K.'s user avatar
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1 vote

Deriving FOC with non-substitable goods

Seems like one would make use of the fact that $M_f$ and $L_f$ are functions of $Q_f$, while the input prices are functions of the respective inputs, then take the first derivative of the goal ...
Giskard's user avatar
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1 vote

Finding the competitive equilibrium in an exchange economy with two perfect complements

Given a pure-exchange economy with $u_A(x_A,y_A)=\min(x_A,2y_A)$, $u_B(x_B,y_B)=\min(2x_B,y_B)$ Endowment of A is $(k_X,k_Y)$ and of B is $(12-k_X,12-k_Y)$ Set of feasible allocations is $\mathcal{F}...
Amit's user avatar
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1 vote

Homogeneity of compensated demand for Leontief (perfect complements) function

Given a utility function $u:\mathbb{R}^L_+\rightarrow\mathbb{R}$, price vector $p\in \mathbb{R}^L_{++}$ and target level of utility $\mu\in\mathbb{R}$, expenditure minimisation problem is defined as ...
Amit's user avatar
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1 vote

Homogeneity of compensated demand for Leontief (perfect complements) function

Since $x({\mathbf p},u)=u$ and $y({\mathbf p},u)=u/2$ do not depend on prices ${\mathbf p}$, homogeneity of degree zero in prices is trivially satisfied for this special case: $x(t{\mathbf p},u)=x({\...
VARulle's user avatar
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1 vote

A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes

We can show if a utility function exhibits complementarity or substitutability just from its function, without having any information about prices. The utility function gives information about the ...
enthusiastic economist's user avatar
1 vote
Accepted

Perfect complements indifference curve

For perfect complements like $u(x,y) = \min( g(x_1), h(x_2))$ the points at which kinks occur are such that $g(x_1)= h(x_2)$. In this case that would be $x= \sqrt(y)$ so in this case indifference ...
1muflon1's user avatar
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1 vote
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Consumer Preference when Consumer only consumes $A$ or $B$

If Sally only prefers A or B but not both, this could be an example of Independent Goods. These are goods that are neither complements nor substitutes, and changes with one good generally do not ...
Jack Bonneman's user avatar
1 vote

hicksian demand of perfect complements

Although one can derive the Hicksian demands by solving the expenditure minimisation problem, but the Leontief function is not differentiable at the 'kink', or at the 'point of optimality'. Thus one ...
superhulk's user avatar
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1 vote
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hicksian demand of perfect complements

Hicksian demand is the consumption bundle that minimizes the expenditure of the consumer subject to the constraint that he attains some target level of satisfaction in equilibrium. In the problem, the ...
Amit's user avatar
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1 vote

Unusual perfect complements utility function min{ax+y, x+2y}

You can solve this question by breaking the Utility function into 2 parts. Use U(x,y) = i) 6x+y if 6x+y < x+2y ii) x+2y if x+2y < 6x+y This would simplify into the Utility Function U(x,y) ...
S.Rana's user avatar
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1 vote

Perfect complement graph and isoquant

$f(x_1,x_2) = \min(x_1,x_2) + x_2 = \begin{cases} x_1 + x_2 & \text{if } x_1 \leq x_2 \\ 2x_2 & \text{if } x_1 > x_2 \end{cases}$ Here is the isoquant map for the production function :
Amit's user avatar
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1 vote

Perfect complement graph and isoquant

An isoquant is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. Having production function: $f(x_1, ...
An economist's user avatar
1 vote

Perfect Complements - Walrasian Equilibrium

Set of feasible allocations is $\mathcal{F}=\{((a_1,b_1),(a_2,b_2))\in\mathbb{R}^2_+\times\mathbb{R}^2_+|a_1+a_2=30 \ \wedge b_1+b_2=20\}$ As can be seen from the picture below, set of competitive ...
Amit's user avatar
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