The Law Of Diminishing Marginal Returns

The Law Of Diminishing Marginal Returns

Total Product (TP) This is the total output produced by workers

Marginal Product (MP) This is the output produced by an extra worker
Definition: Law of Diminishing Marginal Returns

· Diminishing Returns occurs in the short run when one factor is fixed (e.g. Capital)

· If the variable factor of production is increased, there comes a point where it will become less productive and therefore there will eventually be a decreasing marginal and then average product

· This is because if capital is fixed extra workers will eventually get in each other’s way as they attempt to increase production. E.g. think about the effectiveness of extra workers in a small café. If more workers are employed production could increase but more and more slowly.

· This law only applies in the short run because in the long run all factors are variable

· Assume the wage rate is £10, then an extra worker Costs £10.

· The MC of a sandwich will be the Cost of the worker divided by the number of extra sandwiches that are produced

· Therefore as MP increases MC declines and vice versa

· A good example of Diminishing Returns includes the use of chemical Fertilizers a small quantity leads to a big increase in output . Increasing its use further may lead to declining Marginal product

Cross-Price Elasticity of Demand

The Cross-Price Elasticity of Demand measures the rate of response of quantity demanded of one good, due to a price change of another good. If two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases. Similarly if the two goods are complements, we should see a price rise in one good cause the demand for both goods to fall. Your course may use the more complicated Arc Cross-Price Elasticity of Demand formula. If so you'll need to see the article on Arc Elasticity. The common formula for the Cross-Price Elasticity of Demand (CPEoD) is given by:

CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y)

Calculating the Cross-Price Elasticity of Demand
You're given the question: "With the following data, calculate the cross-price elasticity of demand for good X when the price of good Y changes from $9.00 to $10.00." Using the chart below

We know that the original price of Y is $9 and the new price of Y is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded of X when the price of Y is $9 is 150 and when the price is $10 is 190. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=190. You should have these four figures written down:

Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=190

To calculate the cross-price elasticity, we need to calculate the percentage change in quantity demanded and the percentage change in price. We'll calculate these one at a time.

Calculating the Percentage Change in Quantity Demanded of Good X
The formula used to calculate the percentage change in quantity demanded is:
[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

By filling in the values we wrote down, we get:

[190 - 150] / 150 = (40/150) = 0.2667

So we note that % Change in Quantity Demanded = 0.2667 (This in decimal terms. In percentage terms this would be 26.67%).

Calculating the Percentage Change in Price of Good Y
The formula used to calculate the percentage change in price is:
[Price(NEW) - Price(OLD)] / Price(OLD)

We fill in the values and get:

[10 - 9] / 9 = (1/9) = 0.1111

We have our percentage changes, so we can complete the final step of calculating the cross-price elasticity of demand.

Final Step of Calculating the Cross-Price Elasticity of Demand
We go back to our formula of:
CPEoD = (% Change in Quantity Demanded of Good X)/(% Change in Price of Good Y)

We can now get this value by using the figures we calculated earlier.

CPEoD = (0.2667)/(0.1111) = 2.4005

We conclude that the cross-price elasticity of demand for X when the price of Y increases from $9 to $10 is 2.4005.

How Do We Interpret the Cross-Price Elasticity of Demand?
The cross-price elasticity of demand is used to see how sensitive the demand for a good is to a price change of another good. A high positive cross-price elasticity tells us that if the price of one good goes up, the demand for the other good goes up as well. A negative tells us just the opposite, that an increase in the price of one good causes a drop in the demand for the other good. A small value (either negative or positive) tells us that there is little relation between the two goods.
Often an assignment or a test will ask you a follow up question such as "Are the two goods complements or substitutes?". To answer that question, you use the following rule of thumb:

•If CPEoD > 0 then the two goods are substitutes

•If CPEoD =0 then the two goods are independent (no relationship between the two goods

•If CPEoD < 0 then the two goods are complements

In the case of our good, we calculated the cross-price elasticity of demand to be 2.4005, so our two goods are substitutes when the price of good Y is between $9 and $10.

Income Elasticity of Demand

The Income Elasticity of Demand measures the rate of response of quantity demand due to a raise (or lowering) in a consumers income. The formula for the Income Elasticity of Demand (IEoD) is given by:

IEoD = (% Change in Quantity Demanded)/(% Change in Income)

Calculating the Income Elasticity of Demand
On an assignment or a test, you might be asked "Given the following data, calculate the income elasticity of demand when a consumer's income changes from $40,000 to $50,000". (Your course may use the more complicated Arc Income Elasticity of Demand formula. If so you'll need to see the article on Arc Elasticity)Using the chart on the bottom of the page, I'll walk you through answering this question.

Data
Income Quantity Demanded
$20,000 60
$30,000 110
$40,000 150
$50,000 180
$60,000 200

The first thing we'll do is find the data we need. We know that the original income is $40,000 and the new price is $50,000 so we have Income(OLD)=$40,000 and Income(NEW)=$50,000. From the chart we see that the quantity demanded when income is $40,000 is 150 and when the price is $50,000 is 180. Since we're going from $40,000 to $50,000 we have QDemand(OLD)=150 and QDemand(NEW)=180, where "QDemand" is short for "Quantity Demanded". So you should have these four figures written down:

Income(OLD)=40,000
Income(NEW)=50,000
QDemand(OLD)=150
QDemand(NEW)=180

To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time.

Calculating the Percentage Change in Quantity Demanded
The formula used to calculate the percentage change in quantity demanded is:
[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

By filling in the values we wrote down, we get:

[180 - 150] / 150 = (30/150) = 0.2

So we note that % Change in Quantity Demanded = 0.2 (We leave this in decimal terms. In percentage terms this would be 20%) and we save this figure for later. Now we need to calculate the percentage change in price.

Calculating the Percentage Change in Income
Similar to before, the formula used to calculate the percentage change in income is:
[Income(NEW) - Income(OLD)] / Income(OLD)

By filling in the values we wrote down, we get:

[50,000 - 40,000] / 40,000 = (10,000/40,000) = 0.25

We have both the percentage change in quantity demand and the percentage change in income, so we can calculate the income elasticity of demand.

Final Step of Calculating the Income Elasticity of Demand
We go back to our formula of:
IEoD = (% Change in Quantity Demanded)/(% Change in Income)

We can now fill in the two percentages in this equation using the figures we calculated earlier.

IEoD = (0.20)/(0.25) = 0.8

Unlike price elasticities, we do care about negative values, so do not drop the negative sign if you get one. Here we have a positive price elasticity, and we conclude that the income elasticity of demand when income increases from $40,000 to $50,000 is 0.8.

How Do We Interpret the Income Elasticity of Demand?
Income elasticity of demand is used to see how sensitive the demand for a good is to an income change. The higher the income elasticity, the more sensitive demand for a good is to income changes. A very high income elasticity suggests that when a consumer's income goes up, consumers will buy a great deal more of that good. A very low price elasticity implies just the opposite, that changes in a consumer's income has little influence on demand.
Often an assignment or a test will ask you the follow up question "Is the good a luxury good, a normal good, or an inferior good between the income range of $40,000 and $50,000?" To answer that use the following rule of thumb:

•If IEoD > 1 then the good is a Luxury Good and Income Elastic
•If IEoD <> 0 then the good is a Normal Good and Income Inelastic
•If IEoD < 0 then the good is an Inferior Good and Negative Income Inelastic

In our case, we calculated the income elasticity of demand to be 0.8 so our good is income inelastic and a normal good and thus demand is not very sensitive to income changes.

The Budget Constraint

A. The budget constraint defines the set of
baskets that a consumer can purchase with
a limited amount of income.

For convenience, we will consider only the
case of 2 goods (x and y), since we can graph
the budget constraint in this case.

B. Budget set is the set of all baskets that
are affordable, i.e., all (x, y) such that Pxx +
Py y ≤ I, with x ≥ 0, y ≥ 0.

C. Budget line is the set of baskets that cost
exactly the consumer’s income I, i.e., the set
of (x, y) such that
Pxx + Py y = I.

D. Example: Suppose a consumer, Eric, purchases only two goods: food and clothing.
Let x be the number of units of food he
purchases each month and y the number of
units of clothing.

The price of a unit of food is Px, and the
price of a unit of clothing is Py . Assume
that Eric has a fixed income of I dollars per
month.

Eric’s total monthly expenditure on food will
be Px · x (the price of a unit of food times
the amount of food purchased).
Similarly his total monthly expenditure on
clothing will be Py · y.

The budget line indicates all of the combinations of food (x) and clothing (y) that Eric
can purchase if he spends all of his available
income on the two goods. It can expressed
as
Px x + Py y = I

Figure shows the graph of a budget line
for Eric based on he following assumptions:
I = $800, Px = $20 and Py = $40. The
equation of the budget line is
20x + 40y = 800.
Eric can buy any basket on or inside the budget line (A, C, F etc.), but he cannot afford
a basket outside the budget line (G).

Figure 2.1 Eric’s Budget Constraint

How Does the Budget Line Change?

When prices and/or income change, the budget constraint also changes, so do the budget line, budget set, and some of the intercepts

How Does a Change in Income Affect
the Budget Line?

Suppose that Eric’s income increases from
$800 to $1000, while Px and Py stay the
same (See Figure 2.2).
When Eric has I1 = $800, the budget line
is BL1 with a vertical intercept of y = 20, a
horizontal intercept of x = 40, and a slope
of −1/2.
When Eric’s income grows to I2 = $1000,
the budget line is BL2 with a vertical intercept of y = 25, a horizontal intercept of
x = 50, and the same slope of −1/2.


In general, an increase (decrease) in income
causes a parallel shift outward (inward) of
the budget line.
The slope of the budget line −Px/Py does
not change, when only income changes.
Both the horizontal and the vertical intercept
increase or decrease at the same ratio.

How Does a Change in Price Affect
the Budget Line?

Consider for example, only Px increases from
$20 to $25. Py and I do not change. The
budget line rotates in toward the origin, from
BL1 to BL2 (see Figure 2.3).

The horizontal intercept shifts from 40 to
32 units. The vertical intercept does not
change because income and the price of clothing are unchanged.
In general, an increase in the price of one
good moves the intercept on that good’s
axis toward the origin.
Conversely, a decrease in the price of one
good would move the intercept on that good’s
axis away from the origin.
In either case, the slope of the budget line
would change, reflecting the new trade-off
between the two goods.

Total Utility and Marginal Utility

People buy goods because they get satisfaction from them. This satisfaction which the consumer experiences when he consumes a good, when measured as number of utils, is called utility. It is here necessary to make distinction between total utility and marginal utility.

Total utility (TU): Total utility is the total satisfaction which a consumer derives from the consumption of a particular good over a period of time. For example, a person consumes five units of a commodity and derives utility from the successive units of a good, his total utility will be,

Marginal Utility (MU): It can also be described as the extra satisfaction which a consumer gets from consuming additional unit of a good. More precisely, it is defined as the, addition to the total utility obtained from the consumption of one more unit. For example, the marginal utility of second glass of water is the change in total utility resulting from consuming the second glass of water.

Thus

Here Change in total utility and change in Consuming an additional unit of a good. It can also be expressed as here means total utility derived from the consumption of n units of a good and is the total utility derived from the consumption of units.

It may here be noted that as a person consumes more and more units of a commodity, the marginal utility of the additional units begins to diminish but the total utility goes on increasing at a diminishing rate. When the marginal utility comes to zero or we say the point of satiety is reached, the total utility is the maximum. If consumption is increased further from this point of satiety, the marginal utility becomes negative and the total utility begins to diminish.

The relationship between total utility and marginal utility is now explained with the help of following schedule and a graph.

Schedule showing marginal utility and total utility

Units of apples consumed daily	Total utility in utils per day	Marginal utility in utils per day
1	7	7
2	11	4 (11-7)
3	13	2 (13-11)
4	14	1 (14-13)
5	14	0 (14-14)
6	13	–1 (13-14)

The above table shows that when a person consumes no apples, he gets no satisfaction. His total utility is zero, In case he consumes one apple a day, he gains seven utils of satisfaction. His total utility is 7 and his marginal utility is also 7. In case he consumes second apple, he gains an extra 4 utils (MU). Thus giving him a total utility of 11 utils from two apples. His marginal utility has gone down from 7 utils to 4 utils because he has a less craving for the second apple. Same is the case with the consumption of third apple. The marginal utility has now fallen to 2 utils while the total utility of three apples has increased to 13 utils (7 + 4 + 2). In case the consumer takes fifth apple, his marginal utility falls to zero utils and if he consumes sixth apple also, the marginal utility is reduced to negative (13 – 14 = –1). It is –1 utils. The table showing total utility and marginal utility is plotted in figure below:

(1) The total.utility curve starts at the origin as zero consumption of apples yields zero utility.

(2) The TU curve reaches at its maximum or a peak of M when MU is zero.

(3) The MU curve falls throughout the graph. A special point occurs when the consumer consumes fifth apple. He gains no marginal utility from it. After this point, marginal utility becomes negative.

(4) The MU curve can be derived from the total utility curve. It is the slope of the line joining two adjacent quantities on the curve. For example, the marginal utility of the third apple is the slope of line joining points a and b. The slope of such a line is given by the formula . Here .

Price Elasticity of Demand

The Price Elasticity of Demand (commonly known as just price elasticity) measures the rate of response of quantity demanded due to a price change. The formula for the Price Elasticity of Demand (PEoD) is:

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

Calculating the Price Elasticity of Demand

You may be asked the question "Given the following data, calculate the price elasticity of demand when the price changes from $9.00 to $10.00" Using the chart below

Data

Price	Quantity Demanded	Quantity Supplied
$7	200	50
$8	180	90
$9	150	150
$10	110	210
$11	60	250

First we'll need to find the data we need. We know that the original price is $9 and the new price is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded when the price is $9 is 150 and when the price is $10 is 110. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=110, where "QDemand" is short for "Quantity Demanded". So we have:

Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=110

To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time.

Calculating the Percentage Change in Quantity Demanded

The formula used to calculate the percentage change in quantity demanded is:

[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

By filling in the values we wrote down, we get:

[110 - 150] / 150 = (-40/150) = -0.2667

We note that % Change in Quantity Demanded = -0.2667 (We leave this in decimal terms. In percentage terms this would be -26.67%). Now we need to calculate the percentage change in price.

Calculating the Percentage Change in Price

Similar to before, the formula used to calculate the percentage change in price is:

[Price(NEW) - Price(OLD)] / Price(OLD)

By filling in the values we wrote down, we get:

[10 - 9] / 9 = (1/9) = 0.1111

We have both the percentage change in quantity demand and the percentage change in price, so we can calculate the price elasticity of demand.

Final Step of Calculating the Price Elasticity of Demand

We go back to our formula of:

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

We can now fill in the two percentages in this equation using the figures we calculated earlier.

PEoD = (-0.2667)/(0.1111) = -2.4005

When we analyze price elasticities we're concerned with their absolute value, so we ignore the negative value. We conclude that the price elasticity of demand when the price increases from $9 to $10 is 2.4005.

How Do We Interpret the Price Elasticity of Demand?

A good economist is not just interested in calculating numbers. The number is a means to an end; in the case of price elasticity of demand it is used to see how sensitive the demand for a good is to a price change. The higher the price elasticity, the more sensitive consumers are to price changes. A very high price elasticity suggests that when the price of a good goes up, consumers will buy a great deal less of it and when the price of that good goes down, consumers will buy a great deal more. A very low price elasticity implies just the opposite, that changes in price have little influence on demand.

Often an assignment or a test will ask you a follow up question such as "Is the good price elastic or inelastic between $9 and $10". To answer that question, you use the following rule of thumb:

• If PEoD > 1 then Demand is Price Elastic (Demand is sensitive to price changes)

• If PEoD = 1 then Demand is Unit Elastic

• If PEoD <>