2) Sometimes goods are sold with non-linear prices. This problemexamines the implications of utility maximizing behavior for the choices ofindividuals in such settings and what those choices reveal about preferences.

a) Consider the case where the price paidper unit varies with the amount purchased. In particular, consider the casewhere the amount paid is given by p0*qfor q≤q0 and p0*q0 +(q-q0)*P1 for q>q0. Describe the individuals choices when p1<p0 and when p1>p0. What can you say about choices in eachof these two cases? What empirical predictions would you make for each case?Why?

b) Now consider the case where the amountpaid is p0*q for q≤q0 and p1*q for q>q0.What can you say about choices in this case? What in particular do you predictwhen P1>P0? What about when P1<P0?

c) Characterize the individual’schoice when the amount paid is p(q)*q for the case where p’(q)≥0. How would youcharacterize the individual’s choice in terms of the individual’s uncompensated or compensated demandcurve? Are there complications in the case where p’(q)<0? Why or why not?

d) Now consider he case where the amountpaid for a good depends on the amount of another good purchased so that theamount paid for this good is p(y)*q, where y is the quantity purchased of theother good. Can you describe this individual’s choice in terms of the individual’suncompensated demand curve for the two goods?

e) Describe how you could use the observedchoices of individuals in parts a and b to learn about the elasticity of demandfor this good. Does the existence of non-linear pricing help you learn aboutthe degree of substitution even with small variation in prices?

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