Question

The market demand and market supply of wooden chairs are given below: Q 30 2P Q 103P (1) (2) (a) Identify which one is the demand equation and why? (b) Identify which one is the supply equation and why? (c) What is the equilibrium price (P) and equilibrium quantity (Q)? (d) Describe the market situation if market price (P) is 6 (e) Describe the market situation if market price (P) is 10

Answer 1

a)

The demand equation is Q = 30 - 2P

By taking the first derivative of the above equation we get:-

dq/dp = -2 ( slope)

A demand equation is downward sloping and has negative slope which means that as price increases of a good the demand for the good decreases. In the equation Q = 30 - 2P,  the demand is maximum when P = 0. As P increases we observe that the demand decreases.

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b)

The supply equation is Q = -10+3P

The first derivative of the above equation gives

dq/dp = 3 ( slope)

A supply curve is upward sloping and has a positive slope which means that as price increases the quantity supplied of a good also increases. In the equation Q = -10+3P, we observe that as P increases, the quantity supplied also increases.

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c)

The equilibrium price and quantity is found by equating the demand and supply curve equations

Q_s = Q_d

-10+3P = 30 - 2P

5P = 40

P = $ 8

Q = 30 - 2P

Q = 30 - 2 x $ 8

Q = 14 units

The equilibrium price is $ 8 and equilibrium quantity is 14 units.

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d)

If the market price is $6

Quantity demand Q_d = 30 - 2 x $ 6

Q_d = 18 units

Quantity supplied Q_s = -10 + 3 x $6

Q_s = 8 units

When the market price is $6, the quantity demanded is greater than the quantity supplied and the market faces a shortage of 10 units.

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e)

If market price is $10

Quantity demand Q_d = 30 - 2 x $10 ( 10 units)

Quantity supplied Q_s = -10 + 3 x $10 ( 20 units)

When the market price is $10, the quantity supplied is greater than the quantity demanded and the market faces an excess supply by 10 units.