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Can help me with part b of this problem?

The demand for wine is given by the equation $QD = 500 – 20P$, where $P$ is the price of wine per litre and $QD$ is the quantity of wine demanded in litres. The supply of wine is given by the equation $QS = 30P$.

a) Solve for the equilibrium quantity and price of wine.

The current equilibrium would be $500 - 20P = 30P$. therefore the equilibrium price is $P=$ $100 and equilibrium quantity is 1500.

b) Suppose that a $1 per litre tax is levied on the wine producers. Calculate the new equilibrium quantity and price of wine after tax.

Is the new supply $QS = 30P + 1$? So the new equilibrium can be obtain from $30P+1 = 500-20P$. But I get decimal places? Or is the equilibrium $30P + 1Q$?

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  • $\begingroup$ I edited some Latex form, but you should check your maths for the a). $\endgroup$ – bilbo_pingouin Jul 20 '16 at 7:56
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For (a) it appears that you made a slight miscalculation; the equilibrium price cannot be $100 since in that case Quantity Demanded = -1500.

For (a) the equilibrium price is $10 and Quantity of 300.

The trick to getting (b) is seeing the viewpoint of the producers and the buyers rather than just applying the maths.

Producers: 30P where P is the price per litre that they actually receive.
Buyers: 500 - 20P where P is the amount that they actually pay.

Since producers now pay an extra $1 per litre in tax, their actual price is one dollar less therefore
Producers with tax is now 30(P-1).

If you work out the equlibrium using the same method as in (a), you will get a price equilibrium of $10.6 with a quantity of 288.

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