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A monopolist maximizes profit. For me, it is usually easier to do this in the quantity space. So you rearange the demand and maximize $$\max_{Q_p,Q_r} \quad P_p(Q_p)Q_p + P_r(Q_r)Q_r - TC(Q_p+Q_r)$$ $$\max_{Q_p,Q_r} \quad (Q_p-10)Q_p + (28-2Q_r)Q_r - 5-2(Q_r+Q_p) -\frac{(Q_r+Q_p)^2}{8}$$ The FOC gives you two equations with two unknowns, $Q_r$ and $Q_p$, ...


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There is one universal "solution" to monopolism without government intervention. Just allow the monopoly to do its worst. It will give very strong incentives to find ways to satisfy needs of potential clients of the monopoly in ways that would diminish market force of the monopoly. Basically it's bet that human creativity will eventually tame (or even kill) ...


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A monopolist prices by setting marginal revenue equal to marginal cost. The marginal revenue depends on demand. If you have a fixed supply in the sense that the quantity offered is always some $q\in \mathbb R$ independent of the price, then you define a market equilibrium such that the demanded quantity at the equilibrium price must be equal to $q$. As a ...


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Existence of rent has nothing to do with whether market is competitive or not. First there are different definitions of rent. As explained in the Palgrave dictionary of economics (Alchian 2017): Rent’ is the payment for use of a resource, whether it be land, labour, equipment, ideas, or even money. The term is often restricted to payment for use of land or ...


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Demand schedule is a table that gives you the quantity demanded at different prices. An example of demand schedule that I found on Wikipedia is shown below: Demand curve is a curve that plots the demand at different prices in the 2D space defined by $Q$ and $P$ (see example picture I took from investopedia below). Demand curve is essentially a plot of ...


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In narrow sense of the word the article was definitely peer reviewed as it was published in Journal of Legal Analysis. But in this narrow sense it was most likely peer reviewed by jurists not economists. In a broader sense of the word there are economists who had a look at the claims as well. For example, review of their book by Levine (2020) in Journal of ...


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Your marginal revenue is not calculated correctly. Marginal revenue $(MR)$ is the derivate of total revenue which is equal price times quantity $TR=PQ$. In your case $TR$ should be: $$TR=(k+aQ)Q \implies MR = \frac{dTR}{dQ} = k+2aQ$$ If the demand is given as: $P = 120−2Q$ then: $$TR= (120-2Q)Q \implies MR = \frac{dTR}{dQ} = 120-4Q $$ Also made a graph for ...


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Your calculation is not wrong. First a more easy and more intuitive way of calculating marginal revenue is just to take derivative of total revenue. Total revenue is price times quantity $TR=P (Q) Q$ where price is still function of quantity as at higher price people demand lower quantity of goods (I am expressing everything in terms of Q since that is the ...


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The argument is based on the famous prisoner dilemma result. For example, consider the following situation. We have firm A and firm B. If they both collude and set high price (high P) they both can get profit $\\\$7$, If A sets high price but B undercuts A (note undercutting is not the same as engaging in dumping see end of answer) then A will earn 0 profit ...


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Natural monopolies may exist because the cost structure is such that the market could not sustain two firms. This is usually explained by large sunk costs and relatively small demand - if there were two firms the average cost for at least one would have to be above the equilibrium price. If there are no sunk costs at all - as set forth in the ideal case of a ...


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In the typical textbook treatment of the two-part tariff model, income effect is ignored/assumed to be negligible. Goldman, Leland, and Sibley (1984) provided detailed comparison of optimal nonlinear pricing strategies (of which two-part tariff is a special case) with and without income effect. Their conclusion is When [income effects] are absent, the aim ...


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Answer to Original Question Assuming Limited Supply In my opinion equating the two is fallacious from outset. The reason for this is that you can have cases where you have both monopoly and limited supply, only limited supply or only monopoly or neither. In addition, these have different implication for firm firm behavior in general depending on market ...


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We could argue about some of your assumptions, but that would lead to unnecessary opinion-based discussion. In a (perfectly) competitive market everyone is a price taker. This is not the case here. Therefore, it is not a perfectly competitive market. However, before this is taken as a reason to radically restructure society and property rights, you should ...


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First of all good question. I tried myself on that one, but if any other member of this wonderful site has additional input please also answer :) In a monopol we know there exists a consumer who would be willing to pay a price for an additional unit of the good that is higher than the additional cost to produce that unit. Possibility of Pareto improvement: ...


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In typical textbook two-part tariff there won't be an income effect because either demand will be just assumed to be given by some function or even if there is a utility function it won't feature budget constraint (e.g. see examples of such simple problems in Belleflamme and Peitz, Industrial Organization: Markets and Strategies pp 227-234). In such cases ...


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If a firm cannot cover costs and make profit then it has no profit motive to develop and sell drug XYZ. So the profit motive is a "cost plus" model. The price must cover costs plus profit whether there is a single buyer or multiple buyers of the output goods. If drug XYZ makes a net profit in a domestic market, and if there is a marginal profit in ...


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Economic (not just monopoly) rent is what is otherwise known as produces surplus. And producer surplus is related to profit via $$\text{Producer Surplus}=\text{Profit}+\text{Fixed Cost}$$ assuming that fixed cost is sunk.


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Leaving aside the cases of platform markets and other externalities and natural monopolies, what people who have no training in economics usually miss is question of the size of the market. It may very well be that there is enough demand for only one company to be profitable with the available technology. If a second company attempted to enter the market, it ...


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Hint. The following are the necessary conditions for profit maximization: Monopoly with 1 plant and 1 market: $MR = MC$ Monopoly with 1 plant and 2 markets: $MR_1=MR_2=MC$ Monopoly with 2 plants and 1 market: $MR = MC_1=MC_2$ I'll let you figure out the rest.


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