Production Possibilities frontier

One of the central principles of economics is that everyone faces tradeoffs because resources are limited. These tradeoffs are present both in individual choice and in the production decisions of entire economies. The production possibilities frontier (PPF, also sometimes called a production possibilities curve) is a simple way to show these production tradeoffs graphically.

Since graphs are two-dimensional, economists make the simplifying assumption that the economy can only produce two different goods. Traditionally, economists use guns and butter as the two goods when describing an economy's production options, since guns represent a general category of capital goods and butter represents a general category of consumer goods.

Combinations of output that are inside the production possibilities frontier represent inefficient production, since an economy could produce more of both goods (i.e. move up and to the right on the graph) by reorganizing resources. On the other hand, combinations of output that lie outside the production possibilities frontier represent infeasible points, since the economy doesn't have enough resources to produce those combinations of goods. Therefore, the production possibilities frontier represents all points where an economy is using all of its resources efficiently. A production possibility frontier (PPF) is a curve or a boundary which shows the combinations of two or more goods and services that can be produced whilst using all of the available factor resources efficiently.

 

Indifferent Curve and its combinations

Utility: a generalized term for the satisfaction obtained by an individual from the 'use' of a product (good or service) measured by the price the individual is willing to pay for the product.

Indifference Curve:

    For any level of utility - U'  = f (x, y) - there is a locus of commodity combinations which graphically form an indifference curve, that is, all combination yield the same level of utility - U' meaning the consumer is 'indifferent' to any combination on the curve.  Usually an indifference curve is 'convex' in shape reflecting the fact that an increase in x can only be obtained by a reduction in y, and vice versa. The amount of y that is traded off to obtain an increase in x but maintaining the same level of utility is called the marginal rate of substitution, i.e., MUy/MUx  

Furthermore, in a sense, the 'f' in U = f (x, y) and 'f' is your taste function which is obviously different than mine or any other consumer and is reflected by different shape of indifference curves and different MRSs.  Anyone's indifference map will, for normal goods, be convex (opening away) from the origin.  The reason is diminishing marginal utility, i.e., at some point you are unwilling to give up x for any more y.  This is the point of inflection for the indifference curve.   The transitivity assumption ensures that curves do not intersect but rather rise

higher and higher.

c) Budget Line:

Given a specific level of income, a budget line shows all commodity combinations of x and and y that can be purchased by a consumer, i.e, .I = PxX + PyY.  One cannot consume above it (not attainable given income and prices) and it would be irrational to consume below it and pocket the cash.  Happiness in this model is only derived from the consumption of goods & services purchased on the market.  Saving money does not count other than as a 'good & service' that increases future consumption by 'selling' money for interest.  The maximum amount of x or y one can afford given income and prices is shown as the intercepts of the budget line and the respective axes.

If income goes up (and x and y are normal goods) a new higher budget line will be available to the consumer parallel to the original.

If the price of x decreases then the angle of the budget line changes and the intercept increases, that is, the consumer can buy more x with the same income The slope of the budget line is also the negative of the price ratio, i.e., - Px/Py.  Thus the price ratio is NOT the slope of the line which would be Py/Px (rise over run).  This formulation of the price ratio is a 'convention' or tradition in economics.  However, it also represents the 'relative price' of x and y at a given point in time, i.e., how many units of x can be bought with one unit of y at current prices, e.g., $1.00/50 cents = a relative price of '2'.

d) Equilibrium:

    The commodity combination which maximizes a consumer's utility is the one on the budget line tangent to the highest indifference curve.   In rare cases - a corner solution - an individual will consume none of a commodity x because no amount of x is worth the cost.  In such cases the consumer's maximum utility is obtained on the y -axis that is no x is consumed.

    Equilibrium occurs where the Budget Line just touches (is tangent to) the highest attainable indifference curve.  This equilibrium  or 'best affordable point' satisfies the following conditions:

Marginal Rate of  Substitution (MRS = MUy/MUx) equals the slope of the Budget Line or its negative, the price ratio - (Px/Py) therefore in equilibrium MUy/MUx = - Px/Py

at this point the 'rationale' consumer has equated the MU per dollar of each commodity consumed, i.e. MUx/Px = MUy/Py  Consumers will tend to remain at this point (or be 'in equilibrium') as long as taste, income and prices remain fixed.  This is called the 'initial equilibrium'.  We will now change these assumption one by one and see what happens to equilibrium.

Maximum utility is found where the budget line is tangent to the highest attainable  indifference curve - that is, where the negative slope of the indifference curve (or marginal rate of substitution of x for y) is equal to the slope of the budget line, that is, the marginal rate of substitution equals the (-) price ratio and here MUx/Px = MUy/Py.

2. Manipulations

  From the basic analytic mechanism of the indifference curve and budget line a range of additional information can be deduced including:

a) Income-Consumption Curve

    An increase in income increases the intercepts of the budget line but leaves its slope constant - assuming constant prices.  The locus of tangents of budget lines with indifference curves forms the 'income-consumption curve' or the set of commodity combinations (x, y) purchased as income increases - assuming constant prices and taste.

b) Engel Curve

    The amount of a given commodity (x) purchased at different levels of income, derived from the income-consumption curve, forms the 'Engel' curve.  The shape of an Engel curve depends on the type of commodity and consumer taste - assuming constant prices.  The quantity of a commodity (x) purchased will increase at either an increasing or decreasing rate as income rises - depending on the type of commodity.

c) Price-Consumption Curve

    If the price of one commodity (x) changes a new set of combinations (x, y) is created between the changing tangents of the budget line and indifference curves forming the 'price-consumption curve' for the commodity (x) - assuming constant income and prices of the other commodity (y).  The price-consumption curve shows how much of a commodity (x) is purchased if its price changes - assuming constant income and constant prices for the other good (y).

d) Demand Curve

    The demand curve for a given commodity (x) can be derived from the price-consumption curve showing how much of that commodity (x) is purchased at different prices - assuming constant income and constant prices for the other good (y) (MBB 10th Ed. Figs 6.5Aa & 6.5Ab; MBB 11th Ed. A5a & b; PB 4th Ed. Fig. 9.7; 5th Ed. Fig. 8.7). The shape of the demand curve (x) depends on taste, income and the type of commodity - assuming constant prices for the other good (y).

e) Substitution & Income Effects

    An increase in the price of a given commodity (x) causes the slope of the budget line to increase lowering the level of consumer utility, i.e. a new equilibrium on a lower indifference curve - assuming constant income and constant prices for the other good (y) .  The overall effect is called the 'price effect'.

     If, however, income is increased to maintain the initial level of utility the quantity of the commodity (x) consumed will still decrease as the slope of the budget curve increases in response to the price rise.  This decrease in consumption due to a price increase - varying income to maintain the initial level of utility - is called 'the substitution effect'.  It measures how much less of the now more expensive commodity (x) will be consumed. The difference between the amount of  the commodity (x) consumed - if income is not increased to maintain initial utility - and the amount consumed if income is increased is called the 'income effect'

f) Inferior Goods

    The substitution effect is always negative, that is if the price of a commodity (x) goes up, the quantity consumed goes down.  The income effect can be positive or negative.  For 'normal' goods, an increase in income results in an increase in consumption - assuming constant prices.  If the quantity decreases when income increases - assuming constant prices - the commodity is an 'inferior' good.  In most cases, if the price of an inferior good decreases consumption will still increase if income rises.  

3. Consumer Surplus & Price Index

a) Consumer Surplus

    Consumer surplus is the difference between the maximum a consumer is willing to pay for a total quantity of a commodity (x ) and what the consumer actually pays

b) Consumer Price Index

    A consumer price index measures the combined income effect of price changes of given commodity combination (x, y).  It measures how much income must increase or decrease to purchase the same commodity combination (x, y) at different price levels - through time.

Summary of Demand

In effect, Demand reduces to constrained maximization of our happiness subject to a budget constraint represented by two equations:

1. U = f (x, y)

2. I = PxX + PyY