Y7

Consider an individual whose preferences are described by the following utility function:

Uq1,q2=a q1+ q2

q10, q20, a>0

Describe the function and provide a possible scenario in which the function could be employed to describe the decision of a consumer. Set up the problem of the consumer that targets the maximisation of the utility function U, for given prices p1,p2 and disposable income Y.

Derive the demand analytically and report graphically the demand functions for q1 and q2. Do you expect the consumer to find optimal to spend all income in only one of the two goods? If so, why and under what conditions?

Clearly referring to the scenario that you proposed at point (1) above, explain what kind of public policies could influence parameters a, p1 and Y. Graphically describe the effect on the demand of q2 of a reduction in p1. Support your answer with economic intuition.