2
votes
Accepted
How do I use total derivatives of an implicit function to solve this problem?
Given that $u_{1,2} = 0$, the utility function is additively separable. So we have the problem:
$$
\begin{align*}
\max_{x_1, x_2} u(x_1) + v(x_2) \text{ s.t. } &p_1 x_1 + p_2 x_2 = m \ell\\
& ...
- 9,757
2
votes
Quasiconvex and quasiconcave utility function
Every concave (convex) function is quasiconcave (quasiconvex).
Any nondecreasing transformation of a quasiconcave function is quasiconcave (i.e. if the function $f$ is quasiconcave and $g$ is a ...
- 577
2
votes
Accepted
How to calculate direct utility from indirect utility in this exercise?
To get the Hicksian demand function $h$, you can use Shephard's lemma, which says that
$$h_i(p_1,p_2,u)=\frac{\partial e(p_1,p_2,u)}{\partial p_i}$$
where $e$ is the expenditure function.
To get the ...
- 577
1
vote
How do I determine the degree of substitution affect the change in per capita consumption of a good?
Given the great amount of symmetry in your problem, it can actually be reduced to a problem in only two variables. Let us first show that in the optimum $x_1 = x_2$. Towards a contradiction, assume ...
- 9,757
1
vote
How to find the indirect utility function and the expenditure function through this interesting utility function?
Rather than solving the tangency condition for $x_1$ and substituting into the budget constraint, it is much easier to solve the tangency condition for $x_2$ and substitute into the budget constraint.
...
- 577
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