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2 votes

How can I solve a Utility Maximization problem using the Lagrangian method where the Utility formula has an exogenous constant $a$?

If $a>0$ then $u(x,y)$ is a concave function by sum and domain extension theorem.  The optimal bundle will satisfy the following conditions: $$\begin{eqnarray*}i)& \quad \ \frac{MU_x}{MU_y}= \...
0 votes

How to determine convexity or concavity of an indifference curve?

Just an observation, that is too long for a comment, about a possible source of confusion. Maybe an origin of the problem is a confusion about the signs of the derivatives. You wrote: A utility ...
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1 vote

How to determine convexity or concavity of an indifference curve?

It's hard to be sure without knowing the terminology that your teacher is using, but I think a source of confusion here could be two different definitions of convexity. Firstly, a function is convex ...
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0 votes

Determine if goods are substitutes or Complements based on demand function

The Marshallian demands are functions $x_i(p_1,p_2,m)$. You treat $m$ as an independent variable rather than $p_1 x_1 + p_2 x_2$. Since the demands don’t depend on the cross prices (as they don’t ...
1 vote

How to determine convexity or concavity of an indifference curve?

$U(x,y) = \sqrt{x^2 - y^2}$ indeed has concave indifference curves. As you pointed out, this can be found by setting utility to a constant level $\overline{U}$. $\overline{U} = \sqrt{x^2 - y^2} \iff \...
3 votes

Calculating the Compensating Variation with $M^2$

The left hand side expression corresponds to the new utility with the increased price and new budget $M - \Delta M$. The income is now $M - \Delta M$ because we replaced the old income $M$ with $M - \...
0 votes

Determine if goods are substitutes or Complements based on demand function

U should check this video, it helped me anyway https://www.youtube.com/watch?v=0BJ4GUpvKHQ
3 votes

How to handle multiple lagrange multipliers in a maximization problem?

When we allow for debt, somebody else does the lending. So our debt is an asset for somebody else. From the lender's point of view, a transversality condition arises, related to the holding of assets ...
3 votes

How to handle multiple lagrange multipliers in a maximization problem?

This is less than a full answer but hopefully will be of some help. A general observation is that complex optimization problems do not always have an analytical solution. So although you show a ...
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2 votes

What economic theories describe the phenomenon of zero marginal utility when a resources is given at zero cost?

This can be captured by general models of consumer choice that are used to also analyze market interactions. First, spending time in queue is a cost but I think you meant at no monetary cost. Then ...
  • 48.6k
1 vote

How to correctly calculate my real salary?

As @1muflon1 said in his answer, the term real income is used in economics to denote your income after adjusting for inflation and is only useful if you compare incomes over time. That's probably not ...
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1 vote

How to correctly calculate my real salary?

Real salary is salary adjusted for inflation. If you are not comparing salary over time then current salary is also real salary since you are not comparing two salaries over time. Hence your real ...
  • 48.6k
1 vote
Accepted

Finding consumed quantity using marginal utilities

MU of orange juice is always half that of apple juice, so the consumer always prefers additional apple juice over additional orange juice. Therefore, they will never increase the consumption of orange ...
3 votes
Accepted

State dependent preferences vs state independent preferences in utility theory

Starting from the textbook, I would highly recommend any textbook for stochastic dynamic optimization. Then I would recommend you to get acquainted with markov chains, because it is relatively good ...
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0 votes

Solving for Pareto Efficient Utility Possibility Frontier using constrained optimisation

As we can see all points in the feasible set are pareto optimal and the UPF is the set of all pareto efficient points on the contract curve so the feasible set is the UPF in this case. $$Feasible-set :...
0 votes

Integral in front of utility function

What does instantaneous mean here? It means at particular $t$. If $t$ is continuous then $t$ represents a single instant. In addition is the social welfare function then the sum of all U? It looks ...
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