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"If the new bundle was affordable at old prices, and the new and old bundles aren't equal, then the old bundle must not be affordable at the new prices". In other words, the Weak Axiom of Revealed Preference (WARP) refers to consistent (rational) decision-making. I think the proof is in terms of an 'if then' direct method: The Marshallian demand ...

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Investment demand is part of the IS curve since the goods market is given by: $$Y =C(Y-T) + I(Y,i) +G$$ where $I(Y,i)$ would be called investment demand (which will be some function of output and interest rate e.g. $I(Y,i)= d_1Y-d_2 i$. A sensitivity of investment demand to interest rate would usually be interpreted loosely as simply talking about the ...

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To get back to the original production function just multiply both sides with capital. Here: $$Y/K = A (N/K)^{1.1} = F(N/K,1) \implies Y = AN^{1.1}K^{-0.1} =F(N,K)$$ Also, the marginal product of labor here will be: $$F_N'(N,K) = 1.1 A N^{0.1}K^{-0.1} = 1.1 A (N/K)^{0.1}$$

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As far as I can see this comes just from definitions: As given in MWG definition 1.C.1: The choice structure $(\mathscr{B},C(\cdot))$ satisfies the weak axiom of revealed preference if the following property holds: If for some $B \in \mathscr{B}$ with $x,y \in B$ we have $x\in C(B)$, then for any $B'\in \mathscr{B}$ with $x,y\in B'$ and $y\in C(B')$, we ...

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Just for sake of acknowledgement, please note that the game described in the question is a variation of the famous Ultimatum game. Knowing this can help you get a ton of literature on such games. Further note that your professor has made an extremely important point that coming up with answer is sufficient, solving is not necessary. My answer is also limited ...

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Suppose the probability of an error in the $n$th cycle since the most recent maintenance is $a+bn$, and let the number of tasks (cycles) between maintenance be $x$. I'm assuming here that the tasks can be treated as discrete. The way I would approach the optimization is to calculate both the total maintenance cost and the expected total error cost over some ...

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