# Tag Info

Accepted

### Effect of price on utility

That was tricky. The idea is as follows: First, under standard assumptions, demand is continuous. If you change prices a little bit, demand will not change a lot. In particular, if your excess demand ...
• 12.3k

• 12.3k
Accepted

• 1,899
Accepted

### Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

For part (i), in complete rigor, you should also check the determinants of all the leading principal minors of the bordered Hessian and make sure that they have alternating signs. Your final ...
• 15.4k

### General Equilibrium with Perfect Substitutes

To solve for competitive equilibrium, we can first find the demand : Demand for commodity $X$ by A is $x_A = \frac{5}{p_x}$ if $p_x < 1$, $x_A \in [0,5]$ if $p_x = 1$, $x_A = 0$ otherwise. Demand ...
• 8,466
Accepted

### Blocking Coalitions

Coalition formation is not the same as majority voting. Say, in a single good economy, individual 1 has the entire endowment, so $\mathbf e=(1,0,0,0,0,0)$. Then individual 1 forms a blocking coalition ...
• 15.4k
1 vote

### Finding Cobb-Douglas Hicksian Demand using Duality

I prefer another approach. I use duality to find the cost function and then use Shepard's Lemma to derive the Hicksian demands. I will demonstrate below for the simple 2 good case, rather than ...
• 620
1 vote

### What is the difference between solving for utility maximization separately or aggregately?

Under what constraints is $u_1+u_2$ maximized? The exercise may be about the First Welfare Theorem: a competitive equilibrium is Pareto efficient. In this case, maximizing the sum may be designed to ...
1 vote
Accepted

### Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle?

For case 1, you can argue $z$ will be unique by contradiction: Suppose ad absurdum there is another $z'$ that is feasible (i.e. $p^Tz' =w$) optimal and $z'\neq z$. Then you can consider a convex ...
• 354

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