# Market Equilibrium

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 $30P + 1Q$?

• I edited some Latex form, but you should check your maths for the a). – bilbo_pingouin Jul 20 '16 at 7:56

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.
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.