Answer to Question #153856 in Microeconomics for Kareena

Question

(a) In a market, demand and supply curves are defined by the following equations: P=50 - 0.25QD QS= -10 + 2P Where, P is the price in pounds, QS is the quantity supplied and QD is the quantity demanded. (i) What is the equilibrium price and quantity? Please explain your working out of the answer. [3 marks] (ii) What is the price elasticity at a price of £30? Please explain your working out of the answer. [3 marks] (iii) What do you expect will happen to the total expenditure on this good if the price increases from £30 to £40? Is this expectation confirmed if you calculate the total revenue for each price? [4 marks]

Answer 1

i) P=50 - 0.25QD

QD = 200 - 4P

QS= -10 + 2P 

At equilibrium QD=QS.

200 - 4P = -10 + 2P

210 = 6P

P(equilibrium price) = 35

EQ(equilibrium quantity) = -10 + 2*35 = 60

ii) P = 30

QD = 200 - 4*30 = 80

ED(price elasticity of demand) = |d(QD)/dP| * P/QD = 4 * 30/80 = 1.5

iii) total expenditure = P*QD

Since ED > 1, we expect total expenditure to decrease.

At P=30:

total expenditure = 30*(200 - 4*30) = 2400

At P=40:

total expenditure = 40*(200 - 4*40) = 1600

So, our expectation is confirmed.