measuring the quanity purchased of good Y on the y axis and the quantity purchased pf gppd X on the x axis, a line connecting maximum possible purchases of each (the x and y intercepts) will have a slope that is the relative price of the two goods. it wil be tangent to an indifference curve.
as the price line changes slope reflecting a lower price for X, the consumer will buy more of X (assuming it is a normal good). the new price line will have a new tangent point with a higher indifference curve. the change from the old tangency point to the new reflects the sum of an income effect and a substitution effect. the substitution effect is a movement along the same indifference curve, as one good is substituted for another. the income effect is a movement to a higher indifference curve as higher income allow more purchases of both goods.
for a demand curve the point price elasticity of demand is = x/y times dy/dx, dy/dx = the derivative of y at the point (x,y)
the point elasticity = the % change in quantity demanded divided by the % change in price as the changes approach zero
for example if y=4-x is the budget constraint, then if the consumer purchases only good Y, they can buy 4 units of Y. Same result if they purchase only good X, as the maximum they can purchase is 4 units of X. If they purchase 2 units of each, the point cross price elasticity of demand is -1 although the negative sign is usually ignore. It's unit price elasticity at the point (2,2). at point (3,1) the consumer purchases 3 of X and 1 of Y, and the point cross price elasticity = (dy/dx)(x/y) = (-1)(3/1) = -3. at the point (4,0) the point elasticity is (dy/dx)(x/y) = (-1)(4/0) = -infinity. at (0,4) the point elasticy = (dy/dx)(x/y) = -1(0/4) = 0
