Question

The following demand (Q _D) function has been estimated for Fantasy pinball machines:
          
Q _D = 3,500 − 40P + 17.5P _x + 670U + .0090A + 6,500N
  
where P = monthly rental price of Fantasy pinball machines
            P _x = monthly rental price of Old Chicago pinball machines (their largest competitor)
            U = current unemployment rate in the 10 largest metropolitan areas
            A = advertising expenditures for Fantasy pinball machines
            N = fraction of the U.S. population between ages 10 and 30
  
(a)        The point price elasticity of demand (E _D) for Fantasy pinball machines when P = $150, P _x = $100, U = .12, A = $200,000 and N = .35 is  . (round to the second digit after the decimal) {Hint: When you compute Q _D using the provided information, round to the first digit after the decimal.}
(b)        The point cross elasticity of demand with respect to Old Chicago pinball machines for the values of the independent variables given in part (a) is  . (round to the second digit after the decimal)

Answer 1

(a)

Point price elasticity of demand (E_D) is given by :

Here, Q_D = 3,500 − 40P + 17.5P_x + 670U + .0090A + 6,500N

Also it is given that P = $150, P_x = $100, U = 0.12, A = $200,000 and N = 0.35

=> Q_D = 3,500 − 40*150 + 17.5*100 + 670*0.12 + .0090*200,000 + 6,500*0.35 = 3405.4

Thus using above information we have :

Hence, Point price elasticity of demand (E_D) = -1.76

(b)

Point Cross price elasticity of demand (E_C) with respect to Old Chicago pinball machines is given by :

Here, Q_D = 3,500 − 40P + 17.5P_x + 670U + .0090A + 6,500N

Also it is given that P = $150, P_x = $100, U = 0.12, A = $200,000 and N = 0.35

=> Q_D = 3,500 − 40*150 + 17.5*100 + 670*0.12 + .0090*200,000 + 6,500*0.35 = 3405.4

Thus using above information we have :

Hence, Point cross price elasticity of demand (E_C) with respect to Old Chicago pinball machines = 0.51