the maker of a leading brand of low calorie microwavable food estimated the following demand equation for its product

Question

the maker of a leading brand of low calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April_Q= -5200-42P+20pX+5.2i+0.20A+0.25M(2002) (17.5) (6.2) (2.5) (0.09) (0.21)Assume the following values for the independent variables_Q= quantity sold per monthP(in cents)=price of the product =500Px(in cents)=price of leading competitors product =600i (in dollars)= per capita income of the standard metropolitan statistical area(SMSA) in which the supermarket is located =5500A(in dollars)=monthly.

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Solution: (a) Elasticity of demand is calculated using specified formula Elasticity= (IV/Q)(dQ/dIV) Where Q is demand function and IV is some demand determinant; dQ/dIV is first derivative of demand function with respect to determinant. Since our demand function is linear hence coefficient of each IVs in demand function will be first derivatives of demand function with respect to that variable. ( e.g. first derivative of demand function Q with respect to price P will be (-42) i.e. dQ/dP=-42) Value of IVs are given. Q can be calculated by putting these values of IVs in demand function and this gives Q=17650. Now, here we have 5 independent variables as determinant of demand, elasticity of demand for each of the variable is calculated in tabular form for compact presentation. Calculation of elasticity 1 2 3 4=2/3 5 6=4*5 Independent Variable (IV) Values of IVs Dependent Variable (Demand Function Q) IV/Q dQ/dIV Elasticity wrt IV=(IV/Q)* dQ/dIV P P=500 Q= -5200-42P+20pX+5.2i+0.20A+0.25M For given values of independent variables Q= -5200-42*500+20*600+5.2*5500+0.20*10000+0.25*5000 Q=17650 P/Q = 0.028329 dQ/dP = -42 (P/Q)*(dQ/dP)= -1.1898 Px Px=600 Px/Q = 0.033994 dQ/dPx = 20 (Px/Q)*(dQ/dPx)=0.679887 I i=5500 i/Q =0.311615 dQ/di = 5.2 (i/Q)*( dQ/di)=1.620397 A A=10000 A/Q =0.566572 dQ/dA = 0.2 (A/Q)*( dQ/dA)=0.113314 M M=5000 M/Q =0.283286 dQ/dM = 0.25 (M/Q)*( dQ/dM)=0.070822 (b) Interpretation of various elasticities Independent Variable (IV) Elasticity(e) wrt IV Interpretation P

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the maker of a leading brand of low calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April_Q= -5200-42P+20pX+5

Expert Solution

Archived Solution

1	2	3	4=2/3	5	6=4*5
Independent Variable (IV)	Values of IVs	Dependent Variable (Demand Function Q)	IV/Q	dQ/dIV	Elasticity wrt IV=(IV/Q)* dQ/dIV
P	P=500	Q= -5200-42P+20pX+5.2i+0.20A+0.25M For given values of independent variables Q= -5200-42500+20600+5.25500+0.2010000+0.25*5000 Q=17650	P/Q = 0.028329	dQ/dP = -42	(P/Q)*(dQ/dP)= -1.1898
Px	Px=600		Px/Q = 0.033994	dQ/dPx = 20	(Px/Q)*(dQ/dPx)=0.679887
I	i=5500		i/Q =0.311615	dQ/di = 5.2	(i/Q)*( dQ/di)=1.620397
A	A=10000		A/Q =0.566572	dQ/dA = 0.2	(A/Q)*( dQ/dA)=0.113314
M	M=5000		M/Q =0.283286	dQ/dM = 0.25	(M/Q)*( dQ/dM)=0.070822

Independent Variable (IV)	Elasticity(e) wrt IV	Interpretation
P	-1.1898	e<1; thus, for low calorie microwavable food is inelastic, total revenue will increase with increase in price.
Px	0.679887	Cross price elasticity is 0.68<1 means demand is relatively inelastic but a 10% decrease in competitors’ price will result in a 6.8 % decrease in demand of the maker.
I	1.620397	Income elasticity is 1.62>1 shows demand is relatively elastic and a rise of 10% in income will result in 16.2 % increase in demand
A	0.113314	Advertising elasticity of demand=0.113<1. Demand is relatively inelastic so rise in monthly advertising expenditure by 10% would result a 1.13% increase in demand.
M	0.070822	.071<1 indicates a 10% increase in number of microwave ovens sold in the SMSA will result in an increase in demand by less than 1 %( exactly 0.71%)