供应和需求Supply and demand

• 企业理论 Theory of the firm
• 信息经济学 Information economics
• 博弈论 Game theory
• 金融经济学 Financial economics
• 市场失灵 Market failure

经济学Economics的研究项目范围

Economic reasoning is rather easy to satirize. One might want to know, for instance, the effect of a policy change-a government program to educate unemployed workers, an increase in military spending, or an enhanced environmental regulation – will be on people and their ability to purchase the goods and services they desire. Unfortunately, a single change may have multiple effects. As an absurd and tortured example, government production of helium for (allegedly) military purposes reduces the cost of children’s birthday balloons, causing substitution away from party hats and hired clowns. The reduction in demand for clowns reduces clowns’ wages and thus reduces the costs of running a circus. This cost reduction increases the number of circuses, thereby forcing zoos to lower admission fees to compete with circuses. Thus, were the government to stop subsidizing the manufacture of helium, the admission fee of zoos would likely rise, even though zoos use no helium. This example is superficially reasonable, although the effects are miniscule.

经济学Economics 课后作业代写

Two people are involved in a dispute. Person 1 does not know whether person 2 is strong or weak; they assign probability $\alpha$ to person 2’s being strong. Person 2 is fully informed. Each person can either fight or yield. Each person’s preferences are represented by the payoff function that assigns the payoff of 0 if they yield (regardless of what the other player chooses) and payoff of 1 if they fight and the opponent yields. If they both fights, payoffs are given by $(-1,1)$ if person 2 is strong and $(1,-1)$ if person 2 is weak.

Find the Bayesian Nash equilibria if :
i. $\alpha<1 / 2$

Solution. First, consider P1 plays a pure strategy. Suppose P1 plays F. P2’s best response is FY. Compare utilities of $F, Y$ for $P 1$ in response to $F Y$ to see whether $F$ is also a best response to FY.
\begin{aligned} &u_{1}(F, F Y)=\alpha(-1)+(1-\alpha) 1=1-2 \alpha \ &u_{1}(Y, F Y)=\alpha 0+(1-\alpha) 0=0 \end{aligned}
Since $\alpha<\frac{1}{2}$, we observe $u_{1}(F, F Y)>u_{1}(Y, F Y)$. Therefore P1’s best response to $F Y$ is also $F$. We conclude $(F, F Y)$ is a BNE as it is a mutual best response for both players in the Bayesian Game. Now, suppose P1 plays Y. P2’s best response is FF Compare utilities of F and Y for P1 in response to $F F$ to see whether $Y$ is also a best response to FF.
\begin{aligned} &u_{1}(F, F F)=\alpha(-1)+(1-\alpha) 1=1-2 \alpha \ &u_{1}(Y, F F)=\alpha 0+(1-\alpha) 0=0 \end{aligned}
We observe P1’s best response is F. Thus there is no mutual best response where P1 plays Y. Now, we consider P1 playing a mixed strategy. Suppose P1 plays $\sigma_{1}$ such that $\sigma_{1}(F)=p, p \in(0,1)$.

We already showed P1’s best response is a pure strategy to both $F F$ and $F Y$. Thus we consider $p=\frac{1}{2}$ and P2 mixes $\sigma_{2}$ between FF with probability $q$ and FY with probability $1-q$. We compare payoffs for player 1 :
\begin{aligned} &u_{1}\left(F, \sigma_{2}\right)=\alpha[q(-1)+(1-q)(1)]+(1-\alpha)[q(1)+(1-q)(1)]=1-2 q \alpha \ &u_{1}\left(Y, \sigma_{2}\right)=0 \end{aligned}
We assumed P1 mixes with $p$. This can be true if and only if $u_{1}\left(F, \sigma_{2}\right)=u_{1}\left(Y, \sigma_{2}\right)$. (i.e. P1 is indifferent between playing F and $Y$ ). Thus it must be $q=\frac{1}{2 \alpha}$. But since $\alpha<\frac{1}{2}$ implies $q>1$, this is a contradiction and we can’t have a BNE in mixed strategies for this case. We conclude the only BNE of this case is $(F, F Y)$