Suppose your indifference curves are all described by equations of the form x y = constant, with a different constant for each indifference curve.
a. Show that for any point P = (x, y), the indifference curve through P has slope −y/x at P. (This requires calculus. If you don't know enough calculus, you can just pretend you've solved this part and go on to part (b).)
b. Suppose that your income is $40, the price of X is $1, and the price of Y is $1. How much X do you buy?
c. Suppose your income and the price of Y remain as above, but the price of X rises to $4. Now how much X do you consume? (Use the same hint as in part (b).)
d. Based on your answers to parts (b) and (c), draw two points on your demand curve for X.
e. After the price of X rises from $1 to $4, suppose that your income rises by just enough to bring you back to your original indifference curve. Now how much X do you buy?
f. When the price of X rises from $1 to $4, how much of the change in your consumption is due to the substitution effect? How much is due to the income effect?