In a two-commodity world, consider the pair of demand functions q 1 = 6p −2 1 p 2 y −1 2 and q 2 = 4p 1 p 2 y where prices and income are functions of √ the independent vari- ables time t and interest rate r, via the equations p 1 = 12t, p 2 = 10rt 2 , and y = 20r. Find the rate of change of quantity demanded, q 1 and q 2 with respect to both time and interest rate when t = 3 and r = 0.1.
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