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Unformatted text preview: monthly) quantities for each product at the current prices, say q1i and q2i at prices p1i and p2i. We
need also the slopes of the demands, how much less demand would be for product 1 if the price of 1 increases for
product 1 and similarly for product 2. But we also need to know how readily consumers switch between products,
how much more demand would be for product 2 if the price of 1 increases for example. The sensitivity of demands to
changes in price might be estimated for prices near the current prices. Suppose these are given to us as elasticities of
demand e11, e12, e21, and e22 at the current prices with eij being the elasticity for demand i with respect to price j.
Then we have two initial quantities and four elasticities given at current prices. Say for example,
2.5; A matrix is treated as a list of its rows, each row given as a list of entries. A matrix can be displayed as a matrix using
the function MatrixForm. The symbolic elasticity matrix as a function of the prices p1 and p2 is defined by
elasticitymatrix p1_, p2_
D q1 p1, p2 , p1
p1 q1 p1, p2 , D q1 p1, p2 , p2
D q2 p1, p2 , p1
p1 q2 p1, p2 , D q2 p1, p2 , p2
a11 p1 a12 p2 a11 p1 a12 p2 q1 p1, p2
q2 p1, p2 a21 p1 ,
p2 a22 p2 ,
b1 a11 p1 a12 p2 , ,
b2 a21 p1 a22 p2 b2 a21 p1 a22 p2 MatrixForm elasticitymatrix p1, p2
a11 p1 a12 p2 b1 a11 p1 a12 p2 b1 a11 p1 a12 p2 a21 p1 a22 p2 b2 a21 p1 a22 p2 b2 a21 p1 a22 p2 The elasticity matrix we want is
elasticityi e11, e12 , e21, e22 2., 1.2 , 1., 2.5 MatrixForm elasticityi
2.5 These elasticities mean that if the price of product 1 increases by 1% (or $1=p1i*0.01), then the demand for product 1
will decrease by about 2% (a change of -40=q1i*e11*0.01 units) and the demand for product 2 will increase by about
1% (or 18=q2i*e21*0.01), while if the price of product 2 increases by 1% (or $1.10=p2i*0.01), then the demand for
product 2 will by about 2.5% (a change of -45=q2i*e22*0.01 units) and the demand for pro...
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This note was uploaded on 07/12/2013 for the course MATH 256 taught by Professor Schantz during the Spring '11 term at Vanderbilt.
- Spring '11