Question

You are the manager of Firm-X and must analyze an estimated log-linear demand function for your firm’s product (any product). Assume that the R-squared for the estimated regression is 0.80. So,

Write out an estimated log-linear demand function that includes the relevant factors that affect the demand for your product (make up the estimated coefficients and their standard errors for the own price of the product and the other factors that affect the demand for your product). Below the estimated coefficients, write out their standard errors in parentheses. Make sure that you attach the right sign to each coefficient in your estimated demand equation.

The price elasticity of demand for your product is

Given 2, is demand elastic or inelastic?

Are the coefficients statistically significant?

Given 3, an increase in the price of your product will cause total revenue to _______.

Explain if you can use the estimated demand equation to forecast the demand of your product.

Answer 1

Let the regression model be ln(Q) = Bo + BIn(P) + B2 In(P.) + B3 In(P) + B4 In(Y) +€ Where Q=quantity demanded, P=price of the product, Pe=price of the complementary product, P =price of the substitute, Y=average income level of the consumers. Assume that the estimated regression equation as: In(Q) = 100 – 2 ln(P) - 1.5 ln(P.) + 1.2 ln(Ps) + 3.25 In(Y) (30.26) (0.33) (0.23) (0.42) (0.67) Where the numbers in parentheses are respective standard errors of the estimated coefficients. Note that the coefficient of own price and the price of complement is negative, which means that a rise in own price or complements reduces the demand and vice versa. Similarly, the sign of substitutes and consumer income is positive, signifying increase in demand due to increase in price of substitutes or consumer income. Since, the demand equation is in log-linear form, the coefficients are the respective elasticities. For example, -2 = which is the own price elasticity (n). In absolute terms, Inl = 2. Since, Inl = 2 > 1, the demand is elastic in nature. An increase in price by 1%, reduces demand by 2% and vice versa.