Question

Q4:- Suppose for a commodity X, demand and supply curves are given by the equations

                             (1)         Qd = 4 - P

                             (2)         Qs = -2+P

(a)  What are the price elasticities of the demand curve and the supply curves at the points P = 1, 2, 3, etc.?

(b)  Suppose for commodity X, the price elasticity of demand is constant throughout the curve. What can you say about the functional form of the demand curve?

Answer 1

When Qd$=$ 1

Qd$=$ 4$-$ P

1$=$ 4$-$ P

P$=$ 3

Qd$=$ 4$-$ 1 $=$ Qd$=$ 3

When Qd$=$ 2

2$=$ 4$-$ P

P$=$ 2

Qd$=$ 4$-$ 2$=$ Qd$=$ 2

When Qd$=$ 3

3$=$ 4$-$ P

P$=$ 1

Qd$=$ 4$-$ 3$=$ Qd$=$ 1

When Qs$=$ 1

Qs$=$ $-$ 2$+$ P

1$=$ $-$ 2$+$ P

P$=$ 3

Qs$=$ $-$ 2$+$ 1$=$ Qs$=$ $-$ 1

When Qs$=$ 2

2$=$ $-$ 2$+$ P

P$=$ 4

Qs$=$ $-$ 2$+$ 2$=$ Qs$=$ 0

When Qs$=$ 3

3$=$ $-$ 2$+$ P

P$=$ 5

Qs$=$ $-$ 2$+$ 3$=$ Qs$=$ 1

b$)$ a constant price elasticity demand means that a price change of one percent results in a quantity change of one percent