Questions tagged [real-analysis]

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1answer
50 views

Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
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2answers
23 views

Real wages fluctuation as per classical economics

I have just started studying Macroeconomics and have noticed that as per the Classical economics, the real wage level will always remain same because any change in price level in the market is ...
3
votes
1answer
40 views

Concavity of Cobb-Douglass Utility Function on Non-Open set

My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for ...
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votes
0answers
30 views

Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
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0answers
28 views

Calculating elasticity between log term and non-log term [duplicate]

Given the following, I am asked to calculate the elasticity of wages with respect to age: $$𝑙𝑛(𝑀_𝑖)=𝛽_1+𝛽_2π‘Žπ‘”π‘’_i+𝛽_3π‘Žπ‘”π‘’^2_𝑖+𝛽_4π‘Œ_𝑖+𝛽_5𝑇_𝑖+𝛽_6π‘€π‘Žπ‘Ÿ_𝑖+πœ–_𝑖$$ How does one ...
1
vote
0answers
22 views

What problems arise when the minimum wage is directly linked to the inflation rate?

For example if the minimum wage is 10, and the inflation for the year is 3%, then next year the minimum wage is 10*1.03 =10.30. the next year, inflation is 5%, so the minimum wage becomes 10.82. The ...
1
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1answer
82 views

Supporting Hyperplane Theorem and quasiconcave utility function

My notes says that if $u(.)$ is strictly quasiconcave and differentiable, by the supporting hyperplane theorem, there exists $p >>0$ and $w \geq 0$ such that $ x = x(p,w)$ $\forall x$. I am ...