1. In a particular market, demand and supply curves are defined by the following equations: P=100– 0.5QD QS= -200 + 2P where, P is the price in pounds, QS is the quantity supplied and QD¬ is the quantity demanded. (a) What is the equilibrium price and quantity? [5 marks] (b) What is the price elasticity of supply at a price of £35? [5 marks]
Question
In a particular market, demand and supply curves are defined by the following equations:
P=100– 0.5QD QS= -200 + 2P where, P is the price in pounds, QS is the quantity supplied and QD¬ is the quantity demanded.
(a) What is the equilibrium price and quantity? [5 marks]
(b) What is the price elasticity of supply at a price of £35? [5 marks]
Solution
(a) To find the equilibrium price and quantity, we need to set the quantity demanded (QD) equal to the quantity supplied (QS) and solve for P.
Given the equations:
P = 100 - 0.5QD QS = -200 + 2P
We can substitute QS for QD in the first equation to get:
P = 100 - 0.5(-200 + 2P) P = 100 + 100 - P 2P = 200 P = 200/2 P = £100
Substitute P = £100 into the second equation to find QS:
QS = -200 + 2(100) QS = -200 + 200 QS = 0
So, the equilibrium price is £100 and the equilibrium quantity is 0.
(b) The price elasticity of supply (Es) is calculated as the percentage change in quantity supplied divided by the percentage change in price. The formula is:
Es = (dQS/dP) * (P/QS)
From the supply equation QS = -200 + 2P, we can find dQS/dP = 2.
Substitute P = £35 into the supply equation to find QS:
QS = -200 + 2(35) QS = -200 + 70 QS = -130
So, the price elasticity of supply at a price of £35 is:
Es = 2 * (35/-130) Es = -0.538
This means that a 1% increase in price will result in a 0.538% decrease in quantity supplied.
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