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The application of mathematical methods to represent theories and analyze problems in economics.

I get that PED varies along linear (strictly speaking, affine) demand curves in a way that for a demand function $Q(P)=\alpha - \beta P$: $$|\epsilon_D|=1 \iff \frac{\alpha}{2\beta}=P \land |\epsilon_ … asked Jun 22 '21 by j3141592653589793238 1answer I want to show that the marginal revenue is negative for monopolists. We assume P(Q) is homogenous of degree 1, so it is linear (affine, strictly speaking): P(Q)=a-bQ. As we know, \frac{dP(Q)}{dQ … asked Jun 28 '21 by j3141592653589793238 1answer Why is the partial derivative of x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2) for p_1$$ \frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \ …
Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income. Now, I haven't heard of the Slutsky equation yet nor the income/substituti …
Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1. By l …
I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I be …