Part-1

You are the owner of a supermarket that wants to understand your clientís preferences so that you can optimally price your products. You record a clientís purchases of two products x₁ and x₂ in 8 different occasions. The following table summarizes the results.

a. Notice observations number 2 and 5. Quantities purchased are the same but prices are not. What does this mean in terms of the marginal rate of substitution at those quantities?

b. Plot the 8 bundles purchased by the individual in a graph.

c. Which type of preferences comes closer to describing this individualís behavior (Cobb-Douglas, Perfect Complements or Perfect Substitutes)?

d. Write down a utility function that represents these preferences fairly well.

Part-2

You record a clientís purchases of two products x₁ and x₂ in 8 different occasions. The following table summarizes the results:

Notice that for observations 1,2 and 3 even though prices did not change for different amounts of income spent by the client, he/she still purchased the same amount of good one in all three occasions. The same can be said for observations 4,5 and 6 and observations 7 and 8.
a. Draw the Engel curves for good 1 and the income expansion paths for the three sets of prices in the table.

b. The preferences underlying this individualís behavior can be represented by one of the three utility functions. Find which one it is and explain why.

c. Based on your answer to part b, complete the following table with your predictions on the clientís purchases for the given prices and income: