Unformatted text preview: duct 1 will increase by
about 1.2% (or 24=q1i*e12*0.01). Product 2 picks up slightly less than half the customers product 1 loses if price 1
increases, while product 1 picks up slightly more than half the customers product 2 loses if price 2 increases. We want
the given elasticities to be the accurate for (infinitesimally) small changes in price at the give prices and quantities, so
instead of computing slopes manually we write out the exact conditions we want to satisfy. We can write the condition
on elasticities as a matrix equation, meaning the matrices match up entry by entry. Together with the initial quantity
conditions this gives 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
m256hw03soln.nb
5
product 2 will by about 2.5% (a change of 45=q2i*e22*0.01 units) and the demand for product 1 will increase by
about 1.2% (or 24=q1i*e12*0.01). Product 2 picks up slightly less than half the customers product 1 loses if price 1
increases, while product 1 picks up slightly more than half the customers product 2 loses if price 2 increases. We want
the given elasticities to be the accurate for (infinitesimally) small changes in price at the give prices and quantities, so
instead of computing slopes manually we write out the exact conditions we want to satisfy. We can write the condition
on elasticities as a matrix equation, meaning the matrices match up entry by entry. Together with the initial quantity
conditions this gives
calibrationconditions
q1 p1i, p2i
q1i,
q2 p1i, p2i
q2i,
elasticitymatrix p1i, p2i
100. a11 110. a12 b1 elasticityi 2000., 100. a21 100. a11 110. a22 1800., 110. a12
, 100. a11 b2 110. a12
100. a21 b1 ,
100. a11 110. a12
110. a22 b1 ,
100. a21 110. a22 b2 2., 1.2 , 1.,...
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 Spring '11
 Schantz
 Math, Supply And Demand, p1, P2i

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