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 $(p_x, p_y=1)$ ...
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3
votes
Accepted
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 ...
- 17k
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, ...
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3
votes
Accepted
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...
- 29.6k
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 ...
- 51
2
votes
Accepted
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 ...
- 8,487
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 $...
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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 ...
- 15.8k
1
vote
Accepted
Competitive equilibrium in a two-person economy with substitutes and complements
Given the economy with two consumers: $u_1=\min(2m_1,h_1)$ and $u_2=m_2+h_2$ with endowment allocation $E=((60,40),(40,60))$, we observe the case where the price ratio is $\frac{p_M}{p_H}\in (0,1)$. ...
- 9,411
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 ...
- 29.6k
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}...
- 9,411
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 ...
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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({\...
- 7,119
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 ...
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 ...
- 57.7k
1
vote
Accepted
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 ...
- 245
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 ...
- 525
1
vote
Accepted
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 ...
- 9,411
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) ...
- 401
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 :
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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, ...
- 201
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 ...
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