Answer to Question #135490 in Microeconomics for HARINI

Question

2. Suppose demand for lunch box is Qp = 40-P / 5 and the supply of it is Qs = P / 5. Calculate the equilibrium price and quantity of lunch box in this district. Show your answer graphically. (4/20) b. If the price of lunch box cannot be set above%2450. Calculate the "shortage" in this market. Explain your answer with a graph. (2/20) Calculate the price elasticities of demand and supply at quantity demanded and quantity supplied under such a condition.

Answer 1

The Demands Function is as follows : $Qp = 40 - \frac{p}{5}$

The Supply Function is as follows : $Qs = \frac{p}{5}$

a) In equilibrium,

Q_p = Q_s

or, $40 - \frac{p}{5}$ $=\frac{p}{5}$

or, $40 = \frac{2P}{5}$

or, $P = 40\times \frac{5}{2}$

or, P = 100

and, the corresponding value of Q is 20 units,

b)-) The shortage of the Quantity is given by  

S = Q_p - Q_s

Now, Q_p at P = 24.50 is 35.1 units

and, Q_s at P = 24.50 is 4.9 units

hence,  Shortage (S) : 35.1 - 4.9 = 30.2 units

c) Now, Price Elasticity of Demand is the percentage change in Demand due to change in Price

Price Elasticity Of Demand = $(d\frac{Qp}{dp})\times \frac{P}{Q}$ at given price and quantity

in this case, $(d\frac{Qp}{dp})$ = $-\frac{1}{5}$ and so price elasticity in the shortage condition is 0.139 ( putting P=24.5 and Q= 35.1)

Price Elasticity of Supply is the percentage change in Supply due to change in Price

Price Elasticity Of Supply = $(d\frac{Qp}{dp})\times \frac{P}{Q}$ at given price and quantity

in this case,  $(d\frac{Qp}{dp})$ =$-\frac{1}{5}$ and so price elasticity in the shortage condition is 1 ( putting P=24.5 and Q= 4.9)