a contour line that maps consumption bundles yielding the same amount of total utility

an individual is always indifferent between any two bundles that lie on the same indifference curve

for a given consumer, there is an indifference curve corresponding to each possible level of total utility

* they never cross

* the farther out an indifference curve lies - the farther from the origin - the higher the level of total utility it indicates (we assume the more the better + only consider consumption bundles for which the consumer is not satiated)

*they slope downward (b/c th more the better, if you consume more of good x you have to consume less of good y to stay in the bundle)

*they have a convex shape  (as you move down the curve to the right it gets flatter and as you move up to the left it gets steeper, convex b/c bowed in toward the origin, arises b/c of diminishing marginal utility)

goods that satisfy all four properties of indifference curves

the vast majority of goods in any consumer's utility function fall into this category

a pair of goods are ordinary goods in a consumer's utility function if they posess two properties: the consumer requires more of one good to compensate for less of the other, and the consumer experiences a diminishing marginal rate of substitution when substituting one good for another

of good R in place of good M is equal to MU_R/MU_M

the ratio of the marginal utility of R to the marginal utility of M

this happens because as you move down the indifference curve, the slope changes and the condition changes. ex: at one point high on the curve you may have all M and no R, so it increases your utility greatly to get some R and you don't mind giving up M(steep slope), but at a certain point you won't want to give up as much M for R because you won't have as much of it (flatter slope)

(if i have restaurants meals vs housing (more rooms))

1. change in total utility due to lower restaurant meal consumption + change in total utility due to higher housing consumption = 0

2. change in total utility due to lower restaurant meal consumptoin = change in utility due to higher housing consumption

3. change in total utility due to a change in restaurant meal onsumption = MU_MxΔQ_M

and

4. change in total utility due to a change in housing consumption = MU_RxΔQ_R

5. along the indifference curve: -MU_MxΔQ_{M =} MU_RxΔQ_R

right side is neg b/c rep loss in total utility from decreased restaurant meal consumption

6. now to find how this translates to the indifference curve, you divide both sides of equation 5 by ΔQ_R and again by -MU_M in order to get the chang in quantity of m and change in quantity of R terms on one side and the MUr MUm terms on the other. this results in:

along the indifference curve: (ΔQ_M/ΔQ_R)=(MU_R/MU_M)

the left side of this equation is the slope of the indifference curve

the right side of the equation is what is gained from one or more room to what is gained from one or more meal

represented by the flattening of the indifference curve as you slide down to the right - which represents the same logic as the principle of diminishing marginal utility

states that an individual who consumes only a little bit of good A and a lot of good B will be willing to trade off a lot of B in return for one more unit of A

an individual who already consumes a lot of A and not much of B will not be willing to make that trade off

between the indifference curve and the budget line holds when the indifference curve and the budget line just touch (the budget line is tangent to the indifference curve)

this condition determines the optimal consumption bundle when the indifference curves have the typical convex shape

1. use (Q_RxP_R)+(Q_MxP_M)=N

where N stands for income, R represents one good and M represents another good

2. to find the slope of the budget line, divide its vertical intercept by its horizontal intercept, the vertical intercept is the point where all income is spent on one good (Q_R=0), solve for Q_M and then do the opposite to solve for Q_R

3. slope of the buget line = -(vertical intercept)/(horizontal intercept)

((N/P_M)/(N/P_R))=-(P_R/P_M)

P_R/P_M

differs from the ordinary price in terms of dollars, because buying one more R requires giving up P_R/P_M quantity of M we can interpret the relative price P_R/P_M as the rate at which one R trades for one M in the market

at the optimal consumption bundle, the marinal rate of substitution between two goods is equal to their relative price

a change in relative price will lead to a change in slope of the budget line

a rise in income will cause the budget line to shift outward, a shrink in income will cause the budget line to shift inward

the slope of the budget line will not change because the relative price of one good in terms of the other does not change

at the optimal consumption bundle:

-(MU_R/MU_M)=(P_R/P_M)

the marginal rate of substitution between any two goods is equal to the ratio of their prices

it becomes the optimal consumption rule

(MU_R/P_R)=(MU_M/P_M)

this tells us that either using the optimal rule or the relative price rule, we find the same optimal consumption bundle

it depends on the shape of a consumer's indifference curves

perfect substitutes: when indifference curves are straight lines, there is only one relative price at which consumers will be willing to purchase both goods; a slightly higher or lower relative price will cause them to buy only one of the two goods. to see where a consumer's demand lies between two possible indifference curves representing two prices, draw a line from the top of the indifference curve with the lower price to the bottom of the other indifference curve.

perfect compliments: when a consumer wants to consume two goods in the same ratio regardless of their price. the grave has indifference curves that are bent at a 90 degree angle so if the budget line moves, the consumer will buy more/less of the items but in the exact same proportions.

if it is a normal good: consumption of both goods fall, optimum consumption bundle falls

if it is an inferior good: consumption of one (or both if they're somehow both inferior) actually increases (shifts right along the new indifference curve), OR one good increases but the other good falls, indidcating that one is a normal good and one is inferior

the OCB falls overall

the budget line shifts inward and becomes steeper

this is because there was first a movement along the original indifference curve as reletive price changes - pure substitution effect. that part shows how consumption would change if given a hypothetical increase in income that compensates her for increase in price of rooms. then the movement inward from the hypothetical indifference curve to the inward indifference curve is the change in consumption when we remove that hypothetical income compensation. it is the income effect of the price increase - how consumption changes as a result of the fall in purchasing power

the substitution effect because even if the income effect moves in the opposite direction of the substitution effect in the case of an inferior good, the substitution effect is still stronger.

ex: after loss of income the budget line shifts down, even if there is an inferior good and you're consuming more of it, the bundle overall consumes less than in the original budget line

a type of inferior good in which the income effect is so strong that it dominates the substitution effect causing the demand curve for that good to slope upward

very rare but it happens sometimes, generally not important when discussing income and substitution effects