Sam views a packet of cheese (good X) and a bottle of wine (good Y) as perfect complements. Each month Sam sets aside 80 to spend on cheese and wine. The prices of the two goods are P_x= P_y = 10.

1. Sketch some of Sam's indifference curves in a diagram and explain their shape.

2. Add Sam's budget line to your diagram. Find the amount of cheese and wine Sam choose to consume and add the optimal bundle to your diagram.

3. Sam is consuming at his optimal bundle when he receives am unexpected gift of two bottles of wine. Will Sam benefit from receiving this gift ? Explain your answer.

4. Sam is consuming as in (2) when the price of cheese falls (the price of a bottles of wine is unchanged). Illustrate in a diagram low how the fall in the price of cheese changes Sam's optimal bundle and decompose the effect of the price fall into a substitution and an income effect, explaining your reasoning.