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Sure there is. In an intermediate microeconomics class, you might deal with two consumers in an exchange economy. In a first semester graduate microeconomics course, you may have to find the Nash equilibrium in a Cournot oligopoly with $n$ firms. Generally, we don't deal with $5000$ firms in a textbook problem, but generalize this in $\mathbb{R}^{n}$. ...

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Hint: $Q$ is a function of $p$, and $p$ is a function of $t$. What do you get when you insert the expression $p=0.04t^2+0.2t+12$ into $Q$?

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The second price auction is not dictatorial, because the outcome is not dependent on a single bidder's report. Although single price auction is strategy-proof $($because the game form is straightforward$)$, has more than three alternatives, and is not dictatorial as we have shown above, it is not a counterexample to Gibbard-Satterthwaite. In ...

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Suppose winning the game gives you a payoff of $1$, and losing gives you a payoff of $0$. There are $3$ board positions as below, and call them $A$, $B$, and $C$ respectively, when it is $x$'s turn to play, and call them $D$, $E$, and $F$ when it is $y$'s turn to play.               ...

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The price supply-function for one unit, without tax, is $P=Q^s+8$. The tax is a unit tax in the amount of $\$t$. Thus the unit price increases by t.$P^s+t=Q^S+8+t$And the demand function is still$Q^d=(80/3) - (1/3)P$Solving for p$(1/3)P=80/3-Q^d\quad | \cdot 3P^d=80-3\cdot Q^d$In equilibrium it has to be$P^s+t=P^dQ+8+t=80-3\cdot Q \quad ...

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You can use this online tool. The demand curves are a-x (blue). For different values of a, you can draw the corresponding demand curves. If you want additionally different supply curves, you can draw up to thee different supply curves. My inputs: a-x (blue) x-2 (red) x-1 (green) a from 8 to 10; incrementing by 2. The graph can be very well improved by ...

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I'd use Share$\LaTeX$ with pgfplots. It takes some time to get used to, but the folks down at $\TeX$ Stack Exchange can help you out.

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There is a related thread here: What is the pure strategy Nash Equilibria of asking your professor to cancel class? 1) Yes, there are $n$ Nash equilibria. Your reasoning is correct. Though I would also argue that suppose nobody asks for a raise. Then a single player can ask for a raise and better his outcome. Thus, a beneficial unilateral deviation is ...

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It means that it is possible to construct a complete set of state contingent claims. For any $x$ ($x$ is dimension $S\times1$) there exist a $z$ such that $x=Rz$.

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I think this is an easier way to solve it. When $L<K$ we can factorize $L$ as follows: $Y=\Big[bL^p \Big(\frac{aK^p}{bL^p}+1\Big)\Big]^{1/p}=b^{1/p} L \Big[\frac{a}{b}\big(\frac{K}{L}\big)^p +1\Big]^{1/p}=b^{1/p} L \Big[\frac{a}{b}\big(\frac{L}{K}\big)^{-p} +1\Big]^{1/p}$ $lim_{p \rightarrow - \infty} Y =L$ , since $b^{1/-\infty}=1$, and $lim_{p ... 1 The 2 conditions for person 1 are:$\Large{\frac{\frac{\partial U_1}{\partial x_{11}}}{\frac{\partial U_2}{\partial x_{12}}}=\normalsize\frac{p_1}{p_2}}\quad \normalsize(1)p_1x_{11}+p_2x_{12}=1\cdot p_1+0\cdot p_2\quad (2)$At the beginning$x_{11}=1$and$x_{12}=0$. That is the reason why the RHS looks like this. ... 1 Point of Equilibrium for Supply and Demand $$D(q_e)=S(q_e)$$ $$\frac{405}{\sqrt{q_e}}=5\sqrt{q_e}$$ $$405=5|q_e|$$ $$|q_e|=\frac{405}{5}=81$$ The next step is to find the market price, which is $$P_{mkt}(q_e)=D(q_e)=S(q_e)=5\sqrt{81}=5\cdot 9=45$$ Therefore, the point of equilibrium is $$(q_e, P_{mkt}(q_e))=(81, 45)$$ Consumer Surplus By ... 1 For context, I grabbed this picture from Wikipedia The red area is the integral of$D(x) - 45$from$0$to$81$. Namely, $$\int_0^{81} \left(\frac{405}{\sqrt{x}}-45\right)\,dx$$ To integrate, write$405/\sqrt{x}$as$x^{-1/2}$and use the formula$\int x^a = x^{a+1}/(a+1)$. To check the answer, you can use Wolfram Alpha: it's$3645$. 1 The statement is assuming$f_l/f_k$is a function of$k/l$(it is in your example; see below), and then the quantity you're interested in is the slope in a log-log plot (or rather 1/slope). If the slope in a log-log plot is constant, then there's a power relationship (where the power equals the slope.) For example, if$g(x) = A x^C$, then$\ln g = \ln A + ...

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A lot of the policy people in the central banks use vector auto-regression (VAR) models of the economy as alternative to structural models that are more firmly rooted in theory. In a VAR, all variables are treated as endogenous, with each written as linear function of its own lagged lagged values and the lagged values of all the other variables. Some of the ...

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