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Questions tagged [perfect-complements]

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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 ...
1 vote
2 answers
43 views

Deriving FOC with non-substitable goods

I'm trying to derive the first-order condition of cost minimization when inputs are non-substitutable. The question is based on the problem raised by Rubens (AER 2021). Suppose firms $f$ produce $Q_{f}...
5 votes
2 answers
2k views

Pure exchange economy with two consumers and non differentiable utility functions

We have a pure exchange economy, two consumers $A,B$ and two goods $x,y$. The utility functions are as follows $$u_A=\min\{x_A,y_A\}\qquad u_B=\min\{x_B,\sqrt{y_B}\}$$ The endowments are $$\omega_A=(...
1 vote
1 answer
244 views

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

I am currently in a Microeconomics class and have come across the problem described below. I have tried to solve the problem algebraically but only get to the intercept (x1a,x2a)=(8,4). I know that ...
0 votes
0 answers
297 views

utility functions of perfect complements

if preferences are described and in this case the preferences are perfect complements, we want to find an utility function that describes the preferences so we can draw an indifference curve. the ...
1 vote
3 answers
4k views

Perfect Complements - Walrasian Equilibrium

For a homework , I struggled to solve the following question but couldn't go further: endowment of person 1 = (30,0) endowment of person 2 = (0,20) utility ...
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 ...
0 votes
2 answers
377 views

Homogeneity of compensated demand for Leontief (perfect complements) function

In my assignment I have a Leontief (perfect complements) function u(x,y)=min(x,2y). Keeping utility fixed, we minimize the expenditure. Since we have a Leontief function, at a fixed level of utility u(...
3 votes
1 answer
579 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 ...
0 votes
0 answers
68 views

How do we show mathematically that the lump sum principle does not apply to perfect complements?

I want to show mathematically that the lump sum principle does not apply to perfect complements. I was able to show it applied with a specific Cobb-Douglas utility function, but I am not sure how to ...
1 vote
1 answer
910 views

Perfect complements indifference curve

What would be the I.C of this function? $u(x,y)=\min(x,√y)$ I understand since it is a perfect complements case it should be "L" shaped but I wanted a more detailed graph.
0 votes
2 answers
2k views

Perfect complement graph and isoquant

$f(x_1,x_2) = min \{x_1,x_2\} + x_2$ if that was the production, what would the isoquant be? Would it simply follow $x_1 = x_2$? I'm not entirely sure what it the graph would look like.
-2 votes
1 answer
6k views

Income effect for complements

Suppose u(x,y)=min(x,2y) and the price of X is 1, the price of Y is 1 and income is $12. If the price of X increases to 2, the income effect is supposed to be -1. I keep getting zero for some reason. ...
0 votes
1 answer
110 views

What is the reason behind the demand function of a perfect complement good?

so I know that usually the income curve is equal to: $$x_1p_1 + x_2p_2 = m$$ if we rearrange this equation we get that the demand for good one ($x_1$) is equal to: $$x_1 = \frac{m-x_2p_2}{p_1}$$ None ...
2 votes
1 answer
77 views

Consumer Preference when Consumer only consumes $A$ or $B$

Let's say Sally either wants to coke or pizza, but never both. I am aware of the standard consumer preferences, such as Perfect Complements as well as Perfect Substitutes. But I have never heard ...
1 vote
2 answers
11k views

hicksian demand of perfect complements [closed]

As the title states, I want to know how to derive the hicksian demand of perfect complements $\text{min} \, \{x1,x2\}$. Thanks in advance. Also, no price is given, or budget. my main question is ...
0 votes
1 answer
2k views

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

What's the graph for this utility function? How can it be represented graphically? Is this function perfect complements? I do not fully understand that in the question attached in the picture, the ...
1 vote
2 answers
5k views

Relationship between convexity and a perfect complements type utility function

Consider someone who consume two goods and hates them both. Given the utility function: U(x,y)= -max{x,y} 1.What would be the shape of the indifference curve? 2.Why are these preferences weakly ...
1 vote
0 answers
130 views

Elasticity of substitution meaning

If I computed an elasticity of substitution of f.e. 0.9 between capital and labour, does this implicate that the factors are rather well substitutable or not? Since for 0 they are perfect complements ...
0 votes
2 answers
60 views

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

I was not around at this time but I know roads(existing for bikes) and gas(existing for tractors) were complements for cars. I was looking at complements for computers and noticed the ARPANET could ...
6 votes
2 answers
18k views

Perfect complement preferences in an exchange economy

So I have an exam in a bit, I understand that to find the optimal choice you have to equate tangent of the two indifference curves. However, if the other indifference curve is a perfect complement, ...
1 vote
1 answer
615 views

Doubt regarding Walrasian equilibrium with complements for both agents

There are two goods $1,2$ and two agents $ 1,2 $. Both have the utility function $ u_{i}=\min({x_{1i},x_{2i}}) $ for agent $i$ .The endowments are $(1,3)$ and $(3,1)$ for agent $1$ and $2$ ...
0 votes
1 answer
229 views

Optimal consumtion bundle of lemons and sugar [closed]

Alex consumes only lemons and sugar. For each lemon he requires exactly 2 spoons of sugar. He doesn't like more sugar on his lemons, and he won't eat lemons with less sugar. What is Alex's optimal ...
8 votes
1 answer
5k views

Do perfect complements have to be normal goods? If so, why?

Two goods $x,y$ are perfect complements if they have the utility function $$U(x,y) = \min \lbrace ax,by \rbrace $$ $$a,b \in \Bbb{Q}^+$$ My professor said $x,y$ have to be normal goods but didn't ...
3 votes
1 answer
2k views

Basic microeconomics: supply, demand and substitutes in production

The question is: explain the change in the market for skim milk, if demand for ice cream rises. I'd say these two are unrelated in consumption (saying they're substitutes is kind of stretching it), ...