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Elasticity Analysis - Supply and Demand

            
             The first task given by the supervisor is to calculate the elasticities of each independent variable that is present in the model. In order to do so, the partial derivatives for each variable would be calculated. This is done as the partial derivative shows the effect on the dependent variable that is caused by the independent variables. When there are more than one independent variables involved, the best method to do this is to find the effect on the dependent variable caused by each variable individually. In order to show this, each independent variable is taken in isolation. By is isolating this impact, the effect of the independent variable alone can be seen. The partial derivative for model 1 are shown as.
             Price elasticity of demand = ΔQ/δP = -42 + 20X.
             Competitor's price elasticity of demand = ΔQ/δX = 20P.
             Income elasticity of demand = ΔQ/δI = 5.2.
             Advertising elasticity of demand =ΔQ/δA = 0.2.
             Microwave elasticity of demand = ΔQ/δM = 25.
             The same process can be carried out for model two can be shown in the following manner.
             ΔQ/δP = -100 + 25X.
             ΔQ/δA = 15.
             ΔQ/δX = 25P.
             ΔQ/δI = 10.
             Implications of Elasticity.
             The elasticity is the change in quantity demanded based on the change in price that takes place. In regards to the models given, the independent variables would be run through a partial derivation. The partial derivation will give the change in price and the change in quantity that takes place. The explanations for the first model are that ΔQ/δP shows that the model would become -42 + 20X and the remaining factors would be treated as constant and would become zero. This would mean that when there is a one unit change in price, quantity falls by 42 + 20 X where X is the value of leading customer's price. If the price of the competitors is 600 cent, then the fall in quantity would be (-42+60) meaning by 18 units only. This means that the change in quantity of this product is dependent on competitor's price and the price of the product itself.


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