Question

The utility function is given by u (x, y) = α √ x + (1 − α) √ y subsjcet to monetary constraint 10=2x+y time constraint, 10=x+2y space constraint 6=x+y ) In an appropriate diagram, illustrate each of the consumers three constraints, and indicate the consumers overall constraint set. Note that the consumer can only purchase a consumption bundle (x, y) if it satisfies all three constraints (i.e., the monetary, time and space constraint). Also, provide a formal description of the overall constraint set. Make sure you label diagrams clearly and include as part of your answer any calculations about the slopes and intercepts of the three constraint lines. (2) In an appropriate diagram, illustrate the consumer's map of indifference curves. Describe how the indifference curves change as α changes. Make sure you label the diagram clearly and include as part of your answer any calculations about the slopes and intercepts of the indifference curves. (3) Formulate and solve the consumer’s utility maximization problem. The only parameter in this problem is α, and your final answer should describe the consumer’s demand for goods X and Y as a function of α. Finally, for what values of α does the consumer (i) spend all of their income, (ii) use up all of their available time, and (iii) use up all of the available space in their vehicle?

Answer 1