Question

(2)The following equations describe the market for commodity X.

Q(p) = 10 + 3P ……………………….(1)

2

Q(p) = 15 – 2P^2 ……………………….(2)

(a)Which of the two equations is the demand equation and which is the supply equation? Explain.

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

(c)Find the price elasticity of demand at equilibrium and comment on how the firm could use this information if it considers a price adjustment that seeks to maximize its total revenue.

(d) Suppose the adoption of a new technology improves the efficiency of producing this product by 3 units, what would be the impact of the new technology on equilibrium price and equilibrium quantity transacted in this market?

(e)Assume a supply shock (prior to the adoption of the new technology) pushes the price of this product $0.75 above equilibrium, comment on the state of instability in this market.

Answer 1

a) Q(p) = 10 + 3P ……………………….(1)

Equation (1) is the supply equation.

Q(p) = 15 – 2P^2 ……………………….(2)

Equation (2) is the demand equation

The slope of supply curve is always positive and in equation 1, the coefficient of price, P (slope of the curve) is positive.

b) Under equilibrium, quantity demanded is equal to quantity supplied

Hence,

10 + 3P = 15 – 2P^2

or, 2P^2 + 3P - 5 = 0

or, (2p+5)(p−1) = 0  

As, price can not be negative. So, P =1

So, Q = 10 + (3*1) = 13 uniits

c) Price Elasticity (e) of quadratic demand function = p/q * dQ/dP = 1/13 * (-4*1) = - 4/13 = - 0.307

The total revenue maximizing price, P depends of elasticity and is given by the relationship below:
MR = P*(1+1/e)

d) Now the quantity has increased to 13+ 3 = 16 units

so the price will change to 10 + 3p = 16

or P = 2

So new equilibrium price is 2 and equilibrium quantity is 16 units

e) If a supply shock pushes the price of this product $0.75 above equilibrium, quantity supplied will get reduced and there will be a deficit in the market.