Question

When the price is $30 per unit, buyers in a market are willing to buy 400 gadgets and when the price is $60 per unit, they are only willing to buy 100 gadgets. When the price is $30 per unit, sellers in a market are only willing to sell 150 gadgets and when the price is $60 per unit, they are willing to sell 225 gadgets. Assume (1) the economic environment of buyers (their income, tastes or preferences, other prices, and expectations) and sellers (technology, input prices, etc.) are constant and (2) the demand and supply curves are linear all along. What is the direct demand equation in this market?

Answer 1

Given the information above, we have two points that lies on the demand curve :

(Q1, P1) = (400, 30) and (Q2, P2) = (100, 60)

Here Q represents the quantity axis and P is the price axis.

Slope of the demand curve (m) = (P2 - P1)/(Q2 - Q1) = (60 - 30)/(100 - 400) = 30/-300 = -(1/10)

Equation of the demand curve :

P - P1 = m (Q - Q1)

Or, P - 30 = -(1/10)(Q - 400)

Or, 10P - 300 = -(Q - 400)

Or, 10P - 300 = 400 - Q

Or, Q = 700 - 10P

Therefore, the direct demand equation is : Q = 700 - 10P