Question

Assume the market for beef is described by the following demand and supply functions:

Q(p) = -6 + 6P…………………………………(1)

2

Q(p) = 50 – 2P…………………………………(2)

(a)Which of the two equations is the demand curve? How did you know?

(b)Find the equilibrium price ($) and equilibrium quantity transacted (000 lb.)in this market.

(c)Determine the price elasticity of demand at equilibrium for this product.

(d)Suppose the adoption of a new technology allows this beef producer to increase supply by 4, how will this affect current equilibrium conditions in this market?

Answer 1

a) As per the law of demand, there exists a negative relationship between the price of the commodity and the quantity demanded. Hence, the demand equation is Q = 50 - 2P

b) Equilibrium is where supply is equal to demand.

Demand = Q = 50 - 2P

Supply = Q = -6 + 6P

50 - 2P = -6 + 6P

8P = 56

P = 7

Price is $7

Q = 50 - 2*7 = 36

Quantity is 36,000 lb.

c) Elasticity of demand = E_d = %change in quantity demanded / %change in price

E_d = (P/Q) * (dQ/dP)

from demand function, dQ/dP = -2

E_d = (7/36) * (-2)

E_d = -0.3889

d) When supply increases by 4, quantity supplied = 36+ 4 = 40

Let Q₁= 40

At Q₁= 40, price in the market would be,

Q = -6 + 6P

Q = Q₁= 40

This will give new price as P₁

40 = -6 + 6P₁

P₁ = 7.67

New Price is $7.67. At P₁ price, quantity demanded is

Q₂ = 50 - (2*7.67)

Q₂ =34.66

New quantity is 34.66

There would be excess supply in the market at P₁ = 7.67

Excess supply =  Q₁ - Q₂ = 5.34 or 5,340 lb