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I think the Investopedia article does not use clear terminology which leads to confusion. In Economics, utility can be split across two categories as ordinal and cardinal utility. In the case of ordinal utility assigning numeric values is meaningless. For example, if A is proffered to B, assigning 200 utils to A and 100 utils to B is meaningless because that ...


4

To expand on @1muflon1's answer. The theory of rational addiction assumes that the utility of a consumer at time instance $t$ depends both on current consumption of the addicitve good, say $c_t$, and the consumption of the addictive good in the past. For simplicity say $c_{t-1}$. So at period $t$ the instantaneous utility looks something like: $$ u(c_t, c_{t-...


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$u = \max(x, y)$ represents the preferences over two substitute goods that cannot be consumed together. For example - tea and coffee. In the event that the consumer gets x quantity of tea and y quantity of coffee, consumer choose to consume only one of the them depending on the quantity. He always choose the one that is offered in larger quantity and throws ...


3

Your thinking is correct that, in some ways, $x_1, x_2$ are substitute goods. We define substitute goods which have the following property: $$\left.\frac{\partial x_i}{\partial p_j}\right|_{u=\bar u}>0$$ The case of $U(x_1,x_2)=\max\{x_1,x_2\}$ is that of a boundary solution as the indifference curves are now concave to the origin. So equilibrium solution ...


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It is possible for an addict to be rational. A famous work on this was done by Becker (1988) Theory of Rational addiction. In order for agent to have rational preferences the preferences have to satisfy the following definition (See MWG Microeconomic Theory pp 6): Definition 1.B.1: The preference relation $\succeq$ is rational if it possesses the following ...


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This is trivially not true. Consider simple example of utility: $$u(x) = x^{1/2}$$ Expected utility $E(u(x)) = E[x^{1/2}]$ Inverse utility is $u^{-1} \implies x = u^2 $ clearly generally $E(u) \neq u^{-1} $.


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There are no simple methods for estimating cardinal utility (ordinal utility would be a different matter - you could just observe few of your choices). This is not because cardinal utility would necessary be unmeasurable. Although this is not completely settled question (see Moscati (2018) Measuring Utility: From the Marginal Revolution to Behavioral ...


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AA approach appears to follow two stages: first, "nature" provides which event obtains, which results in the given lottery; second, the lottery is resolved, therefore revealing the intrinsic probabilities. AA suggests to resolve by backward induction. Under usual conditions for vNM utility, agent may define a function for her utility. I found a ...


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