m256hw03soln

01 while if the price of product 2 increases by 1 or

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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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