Question

How can we prove the long linear demand function ? In own price elasticity , cross price elasticity

Log-Linear Demand - General Log-Linear Demand Function: Own Price Elasticity: P Cross Price Elasticity: Py Income Elasticity : βΜ 3-25

Answer 1

Ln Q_x^d = beta_0 + beta_X ln p_X + beta_Y ln p_Y + beta_M ln M + beta_H ln H doublerightarrow Q_x^d = e^beta + beta_X ln p_X + beta_y ln p_Y + beta_M ln M + beta_H ln H doublerightarrow Q_x^d = e^alpha Where alpha = beta_0 + beta_X ln p_X + beta_Y ln p_Y + beta_M ln M + beta_H ln H the sake to solve own price elasticity = beta_X Own price elasticity = delta Q_x^d/delta p_x middot p_x/Q_x^d = d Q_X^d/ dp_x middot p_x/Q_x^d differentiation w r t p_X doubleleftarrow = d e6 alpha/d p_X middot p_x/e^alpha [alpha = beta_0 + beta_X ln p_X + beta_Y ln p_Y + p_M ln M + p_N ln H] = e^alpha middot beta_X middot 1/p_X middot p_X/e^alpha Own price elasticity = p_x