Question

The demand for schedule for beer is Xd=25-P, where Xd is the quantity demanded of beer in millions of barrels per year and P is price in dollars per barrel.

If the supply curve for beer is Xs = -20 +4P, what is the equilibrium price of a barrel of beer?

Calculate and interpret price elasticity of demand and supply at the equilibrium point.

What would the effect on the price of a barrel of beer if a tax of $ 4 per barrel is imposed by the government?

Answer 1

At equilibrium, $Xd= Xs$

$25-p=4p-20$

$4p=45$

$P=9$

$Q=25+P=25-9=16$

Price elasticity of demand at equilibrium$=\frac{price at equilibrium}{Quantity at Equilibrium}×\frac{dQ}{dP}$

$\frac{dQ}{dP}=25-1=24$

Therefore;

$P.E.D=\frac{9}{16}×24= 13.5$

Beer is an elastic product since it P.E.D is greater than 1.

$Change InQuantity= P.E.D×∆In Price.$

$=4×13.5=54$

Thus the quantity supplied will change by 54.