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Efficiency Criteria to provide a public good?

A situation in which the public good is not provided is inefficient; it is possible to make both consumers better off. To see this, let $c_1$ and $c_2$ be to numbers such that $c_1+c_2=100$, $c_1<...
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Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?

Since your question is posed in terms of a firm producing discrete units of a quantity, the answer has to take this discreteness into account. With discrete units, "marginal" refers to the ...
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3 votes
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Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?

Because profit is maximized at MC=MR. If MC<MR, then firm could still earn more profit by producing little bit more. Also firms do earn positive profit at point where MC=MR. Practical example: Firm ...
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1 vote

Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?

We note that until MC actually meets MB, all production is profitable (by logic you've already seen). Since we agree you want to produce everything up until MC=MB, let's point out that might occur in ...
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Majority Voting Game

The proper way of solving for all NE is already specified in comments. But compared to writing down all strategy profiles and then checking, following may be a better way: There are three types of ...
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0 votes
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Majority Voting Game

NOTE: I assume that ties are solved randomly. So, if each voter casts a ballot for a different candidate, then each candidate gets elected with probability 1/3. So, each voter's expected payoff equals ...
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Microeconomics - utility function

For the first part, the optimization problem is $Max_{f,c} f^{0.3}{0.7}$ $s.t. 50f+20c=500$ Solving this we get $f=3, c=17.5$ So total expense on furniture is $150=3*50$ and total expense on clothing ...
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Microeconomics - utility function

How much does she spend in total on furniture, and on clothing? This looks like an optimization problem, so the process is: Budget equation: $I = p_ff + p_cc $ Marginal Utility of Furnitures: $MU_f = ...
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Solow residual with cost minimization, calculus (Roeger, 1995)

Equation (4b) in the paper gives: $$ \Delta mc_t = \frac{E_t N_t W_t}{Y_t G(.)}\Delta w_t + \frac{E_t K_t R_t}{Y_t G(.)} \Delta r_t - \Delta e_t. \tag{I} $$ Next we also have equation (5) in the paper:...
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6 votes
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Does Debreu's representation theorem of ordinal utility require Hausdorff topology?

No. However, the problem can be reduced to representing preferences on a Hausdorff space. Instead of trying to represent a complete preorder on a set, one can try to represent linear orders on the ...
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1 vote

Price elasticity of demand

Consider the demand function (i.e., your equation for the demand curve) $Q=D(p)$. Then, the price elasticity of demand is $$\varepsilon = \frac{\partial Q}{\partial p} \frac{p}{Q} = \frac{p D'(p)}{D(p)...
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3 votes
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Constrained optimization to find utility maximizing allocation

I think you are trying to find a feasible allocation that maximises the sum of the utilities of the two individuals. So we can write the objective function as: \begin{eqnarray*} \max_{x,y} & \ xy^...
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4 votes

Vector meaning within economics

The meaning is same as in mathematics. Indeed price vector $\mathbf{p}$ is just: $$\mathbf{p} = (p_1,p_2, ... , p_n)$$
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0 votes

Two-sided market framework

More of a comment than a fully fledged answer. But my sense is that you should consider the effect of $P_i$ on $q_j$, as well (see Rochet and Tirole (2006, RAND)). Minor notes: the condition is $v_i +...
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1 vote

Example of an economy where Equilibria may not be efficient, where one agent is altruistic

Consider a one commodity, two consumer world with Preferences: $u_1(x_1, x_2) = x_1$ and $u_2(x_1, x_2) = x_1 + x_2$, where $x_i$ is $i$'s consumption of the good. Endowment: Both consumers have 10 ...
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2 votes

What is the assumption behind "indifference curve does not cross"?

Consider any utility function $u: \mathbb{R}^2_+ \rightarrow\mathbb{R}$. Indifference curve for satisfaction level $\mu$ is defined as: $\text{IC}(\mu) = \{(x, y)\in\mathbb{R}^2_+|u(x, y) = \mu\}$ I ...
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2 votes

Convex Preference but Convex Utility

Example given by Herr K. is perfect. Let me give another example of a dis-continuous utility function which is quasi-concave, but not concave. Consider $u:\mathbb{R}^2_+ \rightarrow \mathbb{R}$ ...
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2 votes

Deriving indifference curves

Another way to represent the preference is: \begin{eqnarray*} u(x_1, x_2, x_3) & = & x_1 + x_2 + x_3 - \min(x_1, x_2, x_3) \\ & = & \max(x_2+x_3, x_1+x_3, x_1+x_2)\end{eqnarray*} You ...
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1 vote

Trying to figure out the price elasticity of demand

Price elasticity of demand is defined as: $$e=\frac{dQ}{dP} \frac{P}{Q}$$ For demand curve $y=x^{-b}$ elasticity of demand is given by $$e=-b$$
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2 votes

Two-sided market framework

I made a very elementary error in forgetting that $f_i(v_i=P_j-\gamma_iq_j,\gamma_i) = f_i(\gamma_i|v_i=P_j-\gamma_iq_j)\text{Pr}(v_i=P_j-\gamma_iq_j)$. This is not the same as $f_i(\gamma_i|v_i=P_j-\...
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0 votes

Does continuous preference imply upper-hemi continuous demand correspondence?

I think I find the solution: this short paper includes a generalized version of Berge's Theorem https://www.jstor.org/stable/2526431?seq=1 The binary relation is used instead of utility. The binary ...
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2 votes

Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

If the commodity space is $\mathbb{R}^2_+$ and the preference is Lexicographic, then with the standard budget sets $B=B(p_X, p_Y, M) = \{(x, y) \in \mathbb{R}^2 | p_Xx + p_Yy \leq M\}$ where $(p_X, ...
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2 votes

Road pricing to fix congestion on roads

It would help if you would explain what MSC and MPC are (thankfully Google lens finds it) MPC = Marginal Privat cost F0 is where the cost are starting to become affected by external costs (...
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1 vote
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How to compare the price elasticity of demand from different points by looking at the graph?

There is no general way of determining elasticity from graph, however linear demand function has a property where demand is infinitely elastic at the top and then elasticity monotonously decreases (in ...
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0 votes

When can I assume that a variable is exogenous?

$Performance_i = \beta_0 +\beta_1 Attend_i +\varepsilon_i$ It may be that healthier snacks do not affect attendance, but I would be very concerned making an assumption of the form $Cov(Attend_i, \...
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1 vote

Checking negativity condition in demand system model

Estimating demand equations with OLS is never done due to some major problems (endogeneity, assumptions of homogeneous coefficients for all consumers, assumptions of a linear demand curve). Most ...
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1 vote

What does it mean to control for a variable?

Summarised explanation: Controlling for a variable essentially means you're measuring an independent variable and accounting for its presence to negate/remove its flow-on effects on other variables ...
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