Question

7) The supply and demand functions for a good are respectively QS = 2P – 4 and QD = 60 – 2P + 2I, with I representing income, P the market price, QS the quantity supplied, and QD the quantity demanded. a) If I = 18, determine i) The equilibrium price; ii) The equilibrium quantity. b) Suppose the income increases to I = 22. Determine i) The quantity demanded at the initial equilibrium price; ii) The equilibrium price; iii) The equilibrium quantity.

10) The supply and demand functions for a good are respectively QS = P – 16 and QD = 14 –P, with P representing the market price, QS the quantity supplied, and QD the quantity demanded. Determine the quantity traded in the market.

Answer 1

7.A)if income=18

i)If income is 18 there will be no effect on equilibrium price and quantity as it will effect when there is increase or decrease in the income. So when income is 18, the equilibrium price and quantity will be:-

QD ans QS are given.

We know that quantity demanded equals quantity supplied. So from this,

QD = QS

60-2P = 2P-4

-2P-2P = -4+60

-4P = -64 (eliminate (-))

P = 64/4

P = 16

ii) similarly we can calculate quantity demand i.e... (60-2×16 = 28)

Above graph shows the equilibrium price and quantity i.e... price = 16 and quantity is 28. Equilibrium point is denoted as 'E'. And horizontal axis contains Quantity and vertical axis has price.

B) if income increases to 22

We have to assume that we are talking about normal good which has positive effect on quantiy demanded. When income increases, quantiy demanded also increases. While the price remain same, so consumer tends to increase the quantiy as the same price. This part of increase in demand is income effect which explains why consumer buy more goods at less price.

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i) above graph shows quantiy demanded at initial equilibrium price :- means at increase in price which is 22 what will be the quantiy at previous equilibrium price ( previous equilibrium price was 16 so we have to increase the demand while price remain constant) so the quantiy demanded at initial equilibrium price is = 36.

ii) in above graph there is an new equilibrium at income 22 (dotted demand line) which is representd as S and D1. Quantiy is denoted by Q2 and price is 22. New equilibirium is denoted as E1. with the increase in income the demand increases from D to D1 and 28 to 32.

10. Given:-

Quantiy demanded, Quantity supplied, from this we can calculate price.

But we need to find quantiy traded which is the total value of sale or demand in a market which is calculated as QD+QS. We will take the following equations of QD and QS as:-

We can write quantiy demand as

P = 14-QD

And quantity supply as

P = 16-QS

Taking price equal we will get,

14-QD = 16- QS

14+16 = QD+QS

Or we can write as

30 = 2QT (Quantity traded)

30/2 = QT

15 = QT

Above graph shows the equilibrium price and quantity derived from the given Quantity demanded and Quantity supplied. It is also Quantity traded as well.