Suppose the own price elasticity of demand for the products of an industry is gi

Question

Suppose the own price elasticity of demand for the products of an industry is given by -0.8, and the Rothschild index is given by 0.12. What happens to the demand of a representative firm in this industry, if its price increases by 1%? Suppose the demand function for an industry is given by Qd/T = 200- 9PT Where Q_T^4 is the quantity demanded that this market is facing, and P_T = $15 is the market price. Suppose the elasticity of demand for one of the firms in the market is -6.14: then calculate the Rothschild index.

Explanation / Answer

Rothschild Index = Elasticity of total market / Elasticity of individual firm

(1)

0.12 = - 0.8 / Elasticity of individual firm

Elasticity of individual firm = - 0.8 / 0.12 = - 6.67

So, for the firm, if price increases by 1%, its quantity demanded will decrease by 6.67%.

(2)

Q = 200 - 9P

When P = 15, Q = 200 - (9 x 15) = 200 - 135 = 65

For overall market, Price elasticity of demand = (dQ / dP) x (P / Q)

= - 9 x (15 / 65)

= - 2.08

Firm's elasticity of demand = - 6.14

Rothschild Index = - 2.08 / - 6.14 = 0.34

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