# All Questions

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### Corner solution of the maximization problem

I have the function $$u(c,h,l)=ln(c-a)+bl+dh$$ I know that $a$ is minimum consumption level. ( which means that $c\ge a$ $h$ is working hours. $l$ is Leisure hours. And $c$ is consumption. The ...
4 views

### How to prove that a concave production imply that the input requirement sets are convex?

According to page 7 of this slide, "A convex production set Y implies that the associated input requirement set V(y) is convex". How can one go about proving it?
24 views

### Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen)

This question comes out of Hansen's Econometrics ((https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf)) In section 2.18, we only impose the assumptions of finite variance and $Q_{xx}$ ...
27 views

### Banks providing loans

Banks are providing loans. While granting a loan two scenarios can take place The Loan is repaid The Loan is not-repaid The benefit from a re-payed loan is small profit. (Let's say 5% in general) ...
77 views

### How does a bank create new money when it pays its own staff?

I am reading Ryan-Collins et al. (2013, Where Does Money Come From? A Guide to the UK Monetary and Banking System). I think I understand how banks create new money whenever they make a loan. Using ...
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89 views

### Algebraic approach towards convexity

I have a function: $u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
8 views

### Consumers in the Marketplace

3 questions: How to use income and cross price elasticity to develop pricing strategies in relation to consumer income, substitutes and complements? How can total revenue be improved by ...
20 views

### Are there any other rational preference relations without utility function representations, besides Lexicographic?

It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some ...
15 views

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### Mathematical calculation (easy I guess)

Let’s say we examine a labour market that includes 100.000 people in total. 80,000 employees are paid 100€ and the rest 20.000 are paid with 80. I want to find the average salary in this labour ...
31 views

### How to find change in the optimal choice with a utility function in general form?

Suppose the utility function is represented as $U(x_1,x_2;I)$, where $I$ is the level of information the consumer possesses. How to find the change in the optimal choice of $x_1$ as price of $x_1$ ...
45 views

### Check if a utility function represents a monotone preference

Given a function $u(x_1, x_2) = x_1 +x_2 + \min(2x_1, x_2)$, how do we mathematically prove that it monotonic or not? Is there is a general algebraic technique to show monotonicity of suchlike ...
10k views

### How to show that a homothetic utility function has demand functions which are linear in income

A homothetic utility function is one which is a monotonic transformation of a homogeneous utility function. I am asked to show that if a utility function is homothetic then the associated demand ...
10 views

### calculate magnitude of a recession

I'm doing an exercise from Blanchard Macroeconomics where I'm, apart from other things, asked to calculate the severity of recessions in the US since 1960. The data on the webpage that's referenced is ...
19 views

### Homothetic preferences linear in income

How to prove that $x(p,I)=I \cdot x(p,1)$? I would favor an argument based on showing that these are the $argmax$ to different problems and they coincide rather than using the fact that the MRS are ...
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### Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?

According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
8 views

### Where to find series of capital-output ratio for the US?

While the capital-output ratio is widely used in Macroeconomics as a target in calibration, it is usually just set to be equal to 3, without specifying the data source nor the methodology used to ...
26 views

### How to draw the graph of $u(x) =min\{x_{1}, x_{2}\}$ and $u(x) =max\{x_{1}, x_{2}\}$?

Given the utility function $u(x) =min\{x_{1}, x_{2}\}$, and $u(x) =max\{x_{1}, x_{2}\}$, I know that the indifference curves look like an L shape and inverted L-shaped, respectively. However, I don'...
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### Revenue maximization problem

There are $N>0$ Households in an economy. The government has aim to maximize a weighted average of income by imposing tax on the rich people and redistribute the tax revenue to the labor ones. ...
634 views

### What happens when I leave out empty cells in regression?

I'm using Stata 14.1 to do a regression, and I got a matsize too small error. It gave some more output to tell me possible reasons for this problem, and I think ...
44 views

### Local non-satiation in economics

I am having trouble completely understanding the mathematical definition of non-satiation. I have stated the definition from Wikipedia below. It would be great if someone can graphically explain. ...
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### Are there examples of strategies where a combination of third degree pricing and two-part tariffs are used together?

Of course, I am only interested in instances where the combination of the two strategies ultimately lead to higher profits than if the monopolistic firm had used only one.
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### Does finding real income adjust for inflation?

I have been reading from this textbook which talks about CPI and inflation http://faculty.washington.edu/cnelson/Chap04.pdf On pages 5 and 6, it talks about how they are deflating the nominal ...
27 views

### Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ...
26 views

### Clarification of iterated prisoners dilemma

In the description of an iterated prisoner's dilemma on Wikipedia, it states that in order for a game to be considered iterable, it must conform to the rule 2R > T + S, where R is the reward for ...
14 views

### Do any social welfare functionals meet all of Arrow’s conditions, plus absolute-scale full-comparability, but no other informational condition?

I’ve been trying to think of social welfare functionals which meet all of Arrow’s conditions–––unrestricted domain, weak Pareto, independence of irrelevant utilities, and non-dictatorship (see this ...
216 views

### Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
26 views