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Demand Estimation: Combination Meals due Demand Estimation: Combination Meals Question a The quantity of combination 1 meals demanded per week depends on the meal’s price and advertising expense. Therefore the model can be specified as:
Where Q is the quantity of combination 1 meals consumed from the two hotels per week
P is the price of combination 1 meals
A is the advertising expense
α,β1,β2 are estimators and ε is the error term.
Using the data in table 1, the regression results using excel software are as shown on the table below.
Therefore, the model is estimated as
Question b
The OLS method is suitable for this analysis. Note that, there are two independent variables; P and A which are strictly exogenous. Although the price of the meals is influenced by the prices of competitors, data for competitor’s prices isn’t provided and thus price is taken as given. Secondly, the independent variables are not correlated (Cov (P, A) =0 and Cov (P,ε) = Cov(A, ε)=0). Generally, the model is in line with all other OLS assumptions.
Question c
From the regression analysis, the model was estimated as
Question d
Where α = 100626, implying that holding price and advertising costs constant, 100626 meals will be consumed weekly. The intercept has p-vale of 3.42*10-6 which is less than 0.05, and hence the estimator is statistically significant to the model at 95% confidence
β1= -16392.7, hence holding advertising cost constant, a reduction in price by a unit increases quantity of meals demanded by 16392.7 and vice versa. The negative sign implies a reverse impact. The coefficient is statistically significant to the model (p-value = 0.0023 ˂0.05).
β2 = 1.576 with a p-value of 0.011, means that ceteris paribus, a unit change in advertising costs changes the number of meals consumed by 1.576 in the same direction. The coefficient is statistically significant at a confidence level of 95% but not statistically significant at a confidence level of 99% (0.01 ˂ 0.011˂0.05)
The significant F is not very small (= 0.000551) implying that the model was correctly specified in that β1≠β2≠ 0 (at least one of the coefficient is statistically different from zero.
R squared measures the goodness of fit. From the analysis R2 = 0.2638, which implies that the explanatory variables used only accounts for 26.38% of the changes that Q (dependent variable incurs. This value is too low since a greater percentage of change in q (73.62%) is explained by variables not included in the model, hence terming the model unfit. Moreover, when adjusted for degrees of freedom, P and A account for 23.37% of all changes of Q (adjusted R2 =0.2337)
Question e
In theory, demand is affected by several other factors in addition to price and advertising expenses. Therefore, the model would be improved by increasing the number of exogenous variables.
Question f
Using and the mean values i.e p = 3.5067 and A = 10008.94
Then Q = 100626 - 16392.7 *3.5067 + 1.576 *10008.94
= 58915.80835
The price elasticity is given by
Using the mean values
= - 0.9757
Therefore, a unit percent change in price results to 0.9757% change in quantity demanded in the reverse direction. Note that the percentage change in quantity demand is less than proportionate. Therefore since demand is relatively inelastic, the company can consider increasing prices so as to increase total revenues.
The advertising elasticity of demand can be obtained as;
= 0.26774
A 1% change in advertising cost results to a 0.26% change in number of meals consumed weekly. Notably, demand is relatively inelastic to advertising costs hence the company should minimize their advertising expenses and focus on other strategies that significantly impact on quantity demanded.
Question g
Given p = 4.15 and A = 18,000
Using
Q = 100626 - 16392.7 *4.15+ 1.576 *18,000
= 32624.663
Question h
Given Q = and A = 18,000
And
=
= $6.14
Bibliography
Dwivedi, D. and Dwivedi, D. (2009). Essentials of business economics. Noida, U.P: Vikas Pub. House Pvt. Ltd.