Paul plays video games only with his young daughter and never alone. For this reason, he always buys exactly two controllers with each purchase of a new gaming console. Otherwise he does not get any utility from owning consoles or controllers.

a) Let x1 denote the number of consoles and x2 the number of controllers that Paul owns. Write a utility function u(x1, x2) that expresses Paul's preferences over these goods.

b) Let m denote the amount of money that Paul spends on consoles and controllers, and p1 and p2 their respective per-unit prices. Find Paul's demand function for consoles, x1(m, p1, p2), and controllers x2(m, p1, p2).

c) What is the sign of x1(m, p1, p2)/m (pos, neg, zero?)? What is the economic interpretation of this result? Are consoles a normal or an inferior good for Paul?

d) What is the sign of x1(m, p1, p2)/p1? What is the economic interpretation of this result?

e) What is the sign of x1(m, p1, p2)/p2? What is the economic interpretation of this result?

For the remaining of the question, assume that m = 1, 500, p2 = 25 and p1 decreases from 450 to 250. 1

f) Find the Total, Income and Substitution effect on consoles, associated with the price decrease in consoles. Provide the economic interpretation behind your results.

g) Find the Total, Income and Substitution effect on consoles, associated with the price decrease in consoles. Provide the economic interpretation of your results.

h) Find the Total, Income and Substitution effect on controllers, associated with the price decrease in consoles. Provide the economic interpretation of your results.

i) Verify that the Slutsky equation holds for both goods