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Homework answers / question archive / The demand and supply function for a good are respectively Q=a+bP+cI and Q=d+gP where Q is quantity, P is price and I is income

The demand and supply function for a good are respectively Q=a+bP+cI and Q=d+gP where Q is quantity, P is price and I is income. Comparative statics analysis (read the relevant part of chapter 12 carefully if you are not familiar with this term!) with respect to income I can be conducted in two alternative ways: (i) Explicitly solve for Q and P as a function of I, and then derive dQ/dl and dp/dl; (ii) Directly differentiate the above two equations with respect to I while taking Q and P as a function of I, and then solve the resulting two equations for dQ/dl and dp/dl. (a) Calculate equilibrium quantity and price for this market as a function of the parameters a, b, c, d, g and I. (b) Use your results from part (a) to calculate the comparative statics derivatives dP/dl and do/dl. (c) Now calculate the same derivatives dP/dl and dQ/dl using the comparative statics analysis of supply and demand presented in this chapter (method (ii) described above). You should be able to show that you get the same results in each case.

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