Question

Stonebuilt Concrete produces a specialty cement used in construction of roads. Stonebuilt is a price-setting firm and estimates the demand for its cement by the state department of transportation using a demand function in the nonlinear form: Q=a po MC POR where Q=yards of cement demanded monthly, P= the price of Stonebuilt's cement per yard, M= state tax revenues per capita, and PR = the price of asphalt per yard. The manager at Stonebuilt transforms the nonlinear relation into a linear relation for estimation. The estimation results are presented below: DEPENDENT VARIABLE: LNQR-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: | 64 0.8093 84.872 0.0001 PARAMETER ESTIMATE STANDARD ERROR VARIABLE T-RATIO P-VALUE INTERCEPT LNP LNM LNPR 8.20 -3.54 0.64287 0.7854 4.01 1.64 0.19 0.38 2.04 -2.16 3.38 2.07 0.0461 0.0357 0.0014 0.0439 The estimated demand for cement is... O elastic because Ê = -2.16. O elastic because Ê = -3.54. O inelastic because Ê = -0.357. O elastic because Ê = 8.2. O inelastic because Ê = -0.461.

Answer 1

Answer

The correct answer is (b) Elastic because E = -3.54.

Demand is given by :

Q = aP^bM^cP_R^d

Taking ln on both sides we get :

ln(Q) = ln(aP^bM^cP_R^d) = ln(a) + b*ln(P) = c*ln(M) + d*ln(P_R)

Formulas :

ln(xy) = ln(x) + ln(y) and ln(x^y) = yln(x)

where a, b , c and d are parameters and here ln(a) = intercept = 8.80, b = -3.54 , c = 0.64827 and d = 0.7854

Hence Regression equation is given by :

Q = 8.80 -3.54*ln(P) + 0.64827*ln(M) + 0.7854*ln(P_R) -------------------Demand equation

Elasticity of demand(E) is given by :

$E = \frac{P}{Q}\frac{\partial Q}{\partial P}$

From demand equation we have :

$\frac{1}{Q}\frac{\partial Q}{\partial P} = 0 -3.54/P + 0 + 0$

$=> E = \frac{P}{Q}\frac{\partial Q}{\partial P} = -3.54$

Hence Elasticity of demand(E) = -3.54

Demand is elastic when absolute value of elasticity of demand > 1. Here absolute value of elasticity of demand > 1 => elasticity of demand of cement is elastic.

Hence, the correct answer is (b) Elastic because E = -3.54.