| A | B |
|---|
| Budget Constraint | Defines the set of baskets that a consumer can purchase with a limited amount of income |
| Budget Line | Indicates all of the combinations of goods (e.g. food and clothing) that Eric can purchase if he spends all of his available income on the 2 goods |
| Budget Line: Equation | PxX + PyY (this means... [(Px) x (x)] + [(Py) x (y)]) |
| Budget Line: Calculating | Consumer Eric purchases only 2 types of goods, food and clothing= Let x= # of units of food he purchases each month and y= # of units of clothing= The price of a unit of food is Px, and the price of a unit of clothing is Py= Also, assume Eric has a fixed income of I dollars per month: RESULT: Eric's total monthly expenditure on food will be (Px) x (x) {"the price of a unit of food times the amount of food purchased}= Similarly, his total monthly expenditure on clothing is (Py) x (y) {"the price of a unit of clothing times the number of units of clothing purchased"}: RESULT: The Budget Line will be [(Px) x (x) + (Py) x (y)= I] |
| Budget Line: What can you buy? | Eric's income (e.g. $800 dollars per month) permits him to buy any basket ON or INSIDE the budget line, but he CANNOT buy a basket OUTSIDE the budget line= These 2 sets of baskets (those Eric can and cannot buy) exemplify what is meant by the budget constraint |
| Budget Constraint: Equation | (This equation is somewhat different from the budget line equation) PxX + PyY ≤ I (this means... [(Px) x (x)] + [(Py) x (y)] ≤ I |
| What does the slope of the budget line tell us? | The slope of the Budget Line is ∆y/∆x= The slope of the budget line tells us how many units of teh good on teh vertical axis a consumer must give up to obtain an additional unit of the good on the horizontal axis (****see pg. 102 for example) |
| Budget Line: Slope | (see pg. 102****) The slope of the budget line is [-Px/Py]= If the price of good x is 3 times the price of good y, the consumer must give up 3 units of y to get 1 more unit of x, and the slope is -3= If the prices are equal, the slope of the budget line is -1 (meaning the consumer can always get 1 more unit of x by giving up 1 unit of y) |
| Budget Line: What happens when a consumer's income increases (when the prices of the 2 goods remain unchanged)? | An increase in income shifts the budget line outward in a parallel fashion (i.e. the slopes of the 2 budget lines [i.e. the older one and the newer one] are the same, because the prices of food and clothing are unchanged [∆y/∆x= -Py/Py])= It expands the set of possible baskets from which the consumer may choose |
| Budget Line: What happens when a consumer's income decreases (when the prices of the 2 goods remain unchanged)? | A decreases in income would shift the budget line inward, reducing the set of choices available to the consumer |
| Budget Line: X and Y intercepts | Y-Intercept: I/Py; X-Intercept: I/Px |
| Budget Line: What happens when the price of one good increases (with the price of the other good and the consumer's income remaining unchanged)? | An increase in the price of one good moves the intercept on that good's axis toward the origin= This would change the slope of the budget line (reflecting the new trade-off between the 2 goods) |
| Budget Line: What happens when the price of one good decreases (with the price of the other good and the consumer's income remaining unchanged)? | A decrease in the price of one good would move the intercept on that good's axis away from the origin= This would change the slope of the budget line (reflecting the new trade-off between the 2 goods [EX: compared to the past slope, where it was -1/2 {meaning you had to give up 1/2 unit of y to get 1 more unit of x}, the new slope might be steeper {5/8, meaning you have to give up 5/8 of y to get 1 more x}]) |
| When the budget line rotates in... | The consumer's purchasing power declines because the set of baskets form which he can choose is reduced |
| When the budget line rotates out... | The consumer is able to buy more baskets than before, and we say that the consumer's purchasing power has increased |
| What increases purchasing power? | An increase in income or a decrease in price |
| What decreases purchasing power? | An increase in price or a decrease in income |
| Optimal Choice | Consumer choice of a basket of goods that 1) maximizes satisfaction (utility) while 2) allowing him to live within his budget constraint (i.e. the optimal amount of each good to purchase) |
| How can we determine the consumer's Optimal Choice? | If we assume that a consumer makes purchasing decisions rationally and we know the consumer's preferences and budget constraint |
| Optimal Consumption Basket | Must be located on the budget line= No point inside the budget line can be optimal (because if Eric bought one of these baskets, he would still have income to left over to buy more of the goods...which would make him even happier) |
| SEE PAGE 106!!!!!!!!!! | SEE PAGE 106!!!!!!! |
| What is the optimal choice problem for the consumer? | max(x,y) U(x,y) subject to: PxX + PyY ≤ I; where the notation "max(x,y) U(x,y)" means "choose x and y to maximize utility," and the notation "subject to: PxX + PyY ≤ I" means "the expenditures on x and y must not exceed the consumer's income"= If the consumer likes more of both goods, the marginal utilities of both goods (e.g. food and clothing) are both positive |
| At an optimal basket... | All income will be spent (i.e. the consumer will chose a basket ON the budget line PxX + PyY = I) |
| The slope of the budget line is... | -Px/Py |
| To maximize utility while satisfying the budget constraint, what is the optimal basket? | To maximize utility while satisfying the budget constraint, Eric will choose the basket that allows him to reach the highest indifference curve while being on or inside the budget line |
| If point A is the optimal basket that both maximizes utility and lies on the budget line, what happens if we move along the budget line away from A? | If Eric were to move along the budget line away from A, even by a small amount, his utility would fall because the indifference curves are bowed in toward the origin (i.e. because there is diminishing marginal rate of substitution of x for y) |
| At the optimal basket, describe the budget line and the indifference curve | At the optimal basket A, the budget line is just tangent to the indifference curve= This means that the slope of the budget line (-Px/Py) and the slope of the indifference curve (-MUx/MUy= -MRSx,y) are equal |
| Optimal Basket: Tangency Condition | { [-MUx/MUy] = -MRSx,y = [-Px/Py] } SIMPLY: { MUx/MUy = Px/Py } SIMPLY: MRSx,y= Px/Py |
| Optimal Basket: Tangency Condition Equation | MRSx,y = Px/Py |
| Interior optimum | An optimum at which the consumer will be purchasing a positive amount of both commodities (x>0 and y>0) |
| Where does the optimum occur? | Occurs at a point where the budget line is tangent to the indifference curve |
| At an interior optimal basket... | The consumer chooses commodities so that the ratio of the marginal utilities (i.e. the marginal rate of substitution) equals the ratio of the prices of the goods |
| ***Tangency Condition*** | { MUx/Px = MUy/Py } This form of the tangency condition states that, at an interior optimal basket, the consumer chooses commodities so that the marginal utility per dollar spent on each commodity is the same= Put another way, at an interior optimum, the extra utility per dollar spent on good X is equal to the extra utility per dollar spent on good Y= THUS, at the optimal basket, each good gives the consumer the same "bang for the buck" |
| Applying the consumer's optimal choice problem to when the consumer buys more than 2 goods | For example, suppose the consumer chooses among baskets of 3 commodities= If all goods have POSITIVE Marginal Utilities, then at the optimal basket the consumer will spend all of his income= If the optimal basket is an interior optimum, the consumer will choose the goods so that the marginal utility per dollar spent on all 3 goods will be the same |
| Tangency Condition: Using [MUx/MUy]=[Px/Py] | For this, the 2 must be equal= REASON: If the MUx/MUy is bigger than the Px/Py, then the consumer will be left off willing to give up more y-units than he has to to get 1 more x |
| Tangency Condition: Using [MUx/Px]=[MUy/Py] | If Eric's marginal utility per dollar spent on X is higher than his marginal utility per dollar spent on Y, he should rather take the last dollar he spent on Y and instead spend it on X= REASON: (pg. 108****) |
| Describe the optimal consumption basket when both marginal utilities are positive | An optimal consumption basket will be on the budget line |
| Describe the optimal consumption basket when there is a diminishing rate of substitution | When there is a diminishing marginal rate of substitution, then an INTERIOR OPTIMAL CONSUMPTION BASKET will occur at the tangency between an indifference curve and the budget line |
| (pg. 109***) Optimality: What basket should the consumer choose to maximize utility, given budget constraint limiting expenditures to $800 per month? | (aka Utility Maximization Problem) IN this case, since the consumer chooses the basket of x and y to maximize utility while spending no more than $800 on the two goods, optimality can be described as follows: max(x,y) Utility= U(x,y) subject to: PxX + PyY ≤I= 800 } In this example, the endogenous variables are x and y (the consumer chooses the basket)= The level of utility is also endogenous= The exogenous variables are the prices Px and Py and Income I (i.e. the level of expenditures)= THe graphical approach solves the consumer choice problem by locating the basket on the budget line that allows the consumer to reach the highest indifference curve |
| (pg. 109***) Optimality: What basket should the consumer choose to minimize his expenditure (PxX + PyY) and also achieve a given level of utility U2? | (aka Expenditure Minimizing Problem) Is expressed as { min(x,y) expenditure= PxX + PyY subject to : U(x,y)= U2 } This is called the EXPENDITURE MINIMIZATIONPROBLEM |
| Expenditure Minimization Problem | (Another way of thinking about optimality) Consumer choice between goods that will minimize total spending while achieving a given level of utility |
| Expenditure Minimization Problem: Endogenous vs. Exogenous Variables | In this problem, the endogenous variables are still x and y, but the exogenous variables are the prices Px, Py, and the required level of utility U2= The level of expenditure is also endogenous |
| To find the basket that minimizes expenditure... | We have to find the budget line that is tangent to the indifference curve U2 |
| "Utility Maximization Problem" and "The Expenditure Minimizing Problem" | Are said to be dual to one another= The basket that maximizes utility with a given level of income leads the consumer to a level of utility U2= That same basket minimizes the level of expenditure necessary for the consumer to achieve a level of utility U2 |
| "Utility Maximization Problem" and "The Expenditure Minimizing Problem": Understanding what they are saying | The Maximization problem is saying that at a certain budget, you have to find a certain basket that maximizes utility (this will be the point where you can draw a Utility curve that is tangent to the budget line)= However, the Expenditure Minimizing is saying that if you are content at a certain utility level but want to find the cheapest way to remain at this level, you simply have to find the point that will be tangent to and ON the budget line that you want to spend and that is also still on the Utility curve that you want to remain at |
| Corner Point | A solution to the consumer's optimal choice problem at which some good is not being consumed at all, in which case the optimal basket lies on an axis= Will occur if the consumer cannot find an interior basket at which the budget line is tangent to an indifference curve= If an optimum occurs at a corner point, the budget line may not be tangent to an indifference curve at the optimal basket |
| *****See pg. 111 | ******See pg. 111 |
| *****See pg. 111 | *****See pg. 111 |
| *****See pg. 111 | *****See pg. 111 |
| *****See pg. 111 | *****See pg. 111 |
| When is a corner point optimal? | When a consumer is very willing to substitute one commodity for another |
| What do you do when you want to focus on the consumer's selection of a particular good or service? | It is useful to present the consumer choice problem using a 2-dimensional graph with the amount of the commodity of interest (EX: housing) on the horizontal axis, and the amount of all other goods combined on the vertical axis= The good on the vertical axis is called a COMPOSITE GOOD (because it is the composite of all other goods) |
| Composite Good | A good that represents the collective expenditures on every other good except the commodity being considered |
| What is the price of a unit of the Composite Good? Result | By convention, the price of a unit of the composite good is Py=1; RESULT: Thus, the vertical axis represents not only the number of units Y of the composite good, but also the total expenditure on the composite good (PyY) |
| Optimal Choice of "Housing" (with Composite Good) | (pg. 114-115) The horizontal axis measures the number of units of housing "h"= The price of housing is Ph= If the consumer has an income of I, he could purchase at most I/Ph units of housing (the intercept of the budget line on the horizontal axis)= The vertical axis measures the number of units of the composite good y (all other goods)= The price of the composite good is Py=1; If the consumer were to spend all his income on the composite good, he could purchase I units of teh composite good= Thus the intercept of the budget line on the vertical axis is I, the level of income= The budget line BL has a slope equal to {-Ph/Py= -Ph} = Given the consumer's preferences, the optimal basket is A, where the consumer purchases ha nits of housing and spends ya dollars on other goods |
| Optimal Choice of "Housing": Subsidy | (Is one type of program that might be implemented to increase the consumer's purchases of housing) Is when the consuemr receives an income subsidy of S dollars from the government= Moves the Budget line out from simple I (on the y-axis) to I+S and from I/Ph (Ph being the cost of housing) x-axis intercept to (I+S)/Ph |
| Optimal Choice of "Housing": Voucher | (Is one type of program that might be implemented to increase the consumer's purchases of housing) Is when teh government gives the consumer a voucher of S dollars than can ONLY be spent on housing= (SEE PAGE 116-117 to see how budget line shifts****) |
| Optimal Choice of "Housing": Income Subsidy VS Housing Voucher | For the consumer, there are times when both the voucher and subsidy are equally good, but there are also times when it isn't good... (see pg. 117) |
| PAGE 117****** | PAGE 117****** |
| PAGE 118-119**** | PAGE 118-119**** |
| Composite Good: Borrowing and Lending | (pg. 121) For the graph, the horizontal axis shows the consumer's spending on the composite good this year; since the price of the composite good is $1, the horizontal axis also shows the amount of the composite good purchased this year= Similarly, the vertical axis shows the consumer's spending on the composite good next year, likewise equivalent to the amount of the composite good purchased that year |
| PAGE 121-122***** | PAGE 121-122***** |
| Quantity Discount | Expand the set of baskets a consumer can purchase= They offer things like $11 for the first 9 units of electricity, and $5.50 for each additional unit of electricity |
| Page 123-125*** | Page 123-125*** |
