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Your calculation is correct. We can doublecheck your work with a graphical approach. As shown in the figure below, $CS$ at some arbitrary and not necessarily equilibrium price $p_0$ is the gray-shaded area. If we take the non-integral approach, we get \begin{equation} CS=\frac12\left(\frac{A}a-p_0\right)D(p_0)=\frac12\left(\frac{A}a-p_0\right)(A-ap_0)=\frac{(...


3

Answer to the Question on Welfare The welfare analysis is not as simple as that. First, let us set aside for a second any inequality considerations (we can add them on later but there are some misconceptions about welfare analysis that have to be corrected first). Welfare in supply-demand analysis is conventionally measured by amount of consumer and ...


3

The MU question you quote is poorly worded. Here the proper answer would be: C Indeterminate with the given information First we can visualize it as shown on the diagrams shown below. Consumer surplus is the difference between willingness to pay (given by demand)`and price they actually pay so for all consumers it is the area below demand curve and above ...


3

Although your question is already answered, I am just adding a small interesting detail that might help from doing some math (especially if the demand function is rather complex): See that (for any constant $a$): $$f(x) = \frac{d}{dx}\int_a^x f(x)$$ Now just looking at the definition of CS, we have that $CS'=-D(p)$


2

What is CS and PS out-of-equilibrium at $P=30$: I think that answer to this question lies in misunderstanding the definition's of consumer and producer surplus. The consumer and producer surplus are actually (following Mankiw Principles of Economics, 8th ed, pp 135 and 140 consumer surplus: the amount a buyer is willing to pay for a good minus the amount ...


2

Consider two situations: (i) a price so high that no consumer buys a good, (ii) the market price at which supply and demand are equal. CS=PS=0 in situation (i) and CS>0 and PS>0 in situation (ii). If you move from (i) to (ii) CS increases and PS as well. If you move from (ii) to (i) PS decreases and so does CS. If consumers cannot be forced to buy, the ...


2

The key to this is in the hint. It lets you know supply and demand are both linear, so you need to figure out what the functions of those two curves are. In this case, you have $$ Q_D = 18 - 1.5P $$ $$ Q_S = 3P $$ Plot these on a supply/demand graph (P on the vertical axis, Q on the horizontal), and the consumer surplus is the shaded area (note, it stops at ...


1

I think you are making it unnecessarily hard for yourself. You can calculate the deadweight loss (DWL) simply as the difference between consumer surplus pre-tax and post tax, and also by adding tax revenue as it is not necessarily wasted if government uses it, so that would be: $$DWL = \frac{(A−ap)^2}{2a} - \frac{(A−a(p+t))^2}{2a} +t(A-a(p+t))= A t - \frac{...


1

Consumer surplus in Microeconomics 101 is indeed often used in the way you describe and to illustrate a point about the allocation efficiency of a free market. However, it is important to keep in mind the assumptions and limitations of the framework you describe. First, the case you describe is a partial equilibrium case. This framework does not allow for ...


1

I see a lot of these posts are very complete, and I think a more direct answer might be beneficial here. The supply curve represents the amount that producers are willing and able to sell at. Producer surplus is the space between the existing price and the supply curve. The demand represents the amount that buyers are willing and able to buy at. Consumer ...


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