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How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good? Not sure what you mean. Utility is not interpreted as some biological measure of happiness. A bundle of goods with high utility is prefered by the consumer to bundles with lower utilities. This is all that utility describes; it is a ...


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The profit of a firm $i$ is given by: $$ \pi_i(p) = p q_i - C_i(q_i) $$ where $p$ is the price, $q$_i is the output of firm $i$ and $C_i(.)$ is the cost function which differs across firms. The first order condition gives: $$ p = \frac{\partial C_i(q_i)}{\partial q_i} = MC_i(q_i^\ast) $$ This shows how to obtain the optimal supply of firm $i$, i.e. where $MC(...


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Nuance matters: In the comments under 1muflon1's answer the quote given is The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing to pay for that unit. Willingness to pay reflects the benefit derived from each unit. So the actual claim is not that the demand curve is the same as the ...


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The claim is not that capital decreases marginal productivity, but that the marginal productivity of capital is decreasing. (See "diminishing returns.") That is, the first "unit" of capital increases productivity the most, the second unit still increases it but less so, the third unit increases productivity even less and so on. Thus when ...


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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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I am not sure why you expect method two to work, as generally $$ \frac{\partial F(K,N)}{\partial N} \neq \frac{\partial F(K,N)}{\partial K}\frac{\partial K}{\partial N}. $$ These are partial derivatives. Unless information to the contrary exists $$\frac{\partial K}{\partial N} = 0.$$ You can easily see that these formulas are not connected by calculating the ...


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How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good? It is not. While it sounds somewhat intuititve, the concept of utility as a kind of psychological measure of "happiness" or "satisfaction" is outdated and no longer used in modern microeconomics. Instead of this ...


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Quasi-linear functions There is one special case where the inverse demand curve equals the marginal utility function. This is when the utility function is quasi-linear, i.e. it takes the form: $$ u(x,y) = v(x) + y. $$ In this case, the first order condition is equal to: $$ v'(x) = p_x. $$ Here $v'(x)$ is indeed the inverse demand function and it is also ...


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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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Still, not 100% clear whether I get the question right, but in models with constant returns to scale and decreasing marginal productivity (question to others, are these conditions even necessary?), if firms are price takers in product and labor markets (no pricing power in which case you could look into monopsony models, see for instance the textbook "...


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You can think of it as the marginal benefit per person. The first piece of pizza you eat is amazing, it has a very high marginal benefit. But say you eat five whole pizzas in one sitting and then are immediately offered another slice. That next slice doesn’t seem so appealing, does it? You’re already full and starting to get sick of it. That slice has a low ...


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The Cobb Douglas production function with constants returns to scale $$y = \prod_i x_i^{\alpha_i} = A \prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i} ,$$ where $A:= \prod_i \alpha_i^{\alpha_i}$ annoying constant. Cost minimization with perfect competition $$\min_x \ \ p^\top x\ \lvert \ y = \prod \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i},$$ implies ...


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I figured it out: The first-order condition of the cost minimization problem for, say, material inputs $m_{it}$ gives: $ \lambda \frac{\partial F}{\partial M} = P_M $ Where F is the production function, $P_M$ the material input prices. Multiply by $\frac{M}{F}$ and rearrange, $ \lambda = \frac{P_M M}{\beta_M F} $, where $\beta_M$ is the output elasticity ...


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I do not know where you heard that but it is generally not true that demand curve is equivalent to marginal utility/benefit curve. Consider trivial counter-example: $$U = x^ay^b \text{ s. t. } px+qx=m$$ Where $U$ is the utility of consuming good $x$ and good $y$, $p$ and $q$ are their respective prices and $m$ is the consumer budget. Here clearly the ...


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The solution to question Your Solution is correct. To get the total differential use the following formula $$d{U} = d{f}= \frac{\partial{U}}{\partial{G_1}}d{G_1} + \frac{\partial{U}}{\partial{G_2}}d{G_2}$$


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I assume that the firm is a monopolist. We know the inverse demand function, the fixed costs and the marginal costs: $P(q) = 20 - q$ $MC(q) = 12$ $F = 16$ As the marginal costs are constant, we can compute the total costs function as: $TC(q) = MC\cdot q + F = 12 q + 16$ The average total costs is obtained by dividing by $q$: $AC(q) = \frac{TC(q)}{q} = ...


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Adding major details, such as information asymmetry to the question after answers are posted is poor form in my opinion. In case the original question is lacking - perhaps because too little time was spent considering it - a new question should be posted. If the firms make an agreement to pay lower wages then by definition they are not competing, so what ...


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The cost of advertising is already considered in production, such as when calculating MC=MB. A good example of a familiar product is beer, which has 2 major costs: water and advertising. I'll note that the marginal product of advertising doesn't always have to be in the region with diminishing returns (perhaps when breaking into a market?) but it's not a bad ...


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