# Elasticity of Demand Assignment help

Price **Elasticity of Demand** (PED or Ed) is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price (holding constant all the other determinants of demand, such as income). It was devised by Alfred Marshall.
Price elasticities are almost always negative, although analysts tend to ignore the sign even though this can lead to ambiguity. Only goods which do not conform to the law of demand, such as Veblen and Giffen goods, have a positive PED. In general, the demand for a good is said to be inelastic (or relatively inelastic) when the PED is less than one (in absolute value): that is, changes in price have a relatively small effect on the quantity of the good demanded. The demand for a good is said to be elastic (or relatively elastic) when its PED is greater than one (in absolute value): that is, changes in price have a relatively large effect on the quantity of a good demanded.
Revenue is maximised when price is set so that the PED is exactly one. The PED of a good can also be used to predict the incidence (or "burden") of a tax on that good. Various research methods are used to determine price elasticity, including test markets, analysis of historical sales data and conjoint analysis.

PED is a measure of responsiveness of the quantity of a good or service demanded to changes in its price.The formula for the coefficient of price elasticity of demand for a good is:

## Application of Differentiation in Economics:-->

## Application of Differentiation:- Elasticity of Demand

**Elasticity of demand:-**If x = f(p) is the demand function, where x is demand and p is the price , then the elasticity of demand is η

_{d = }p . dx But demand is a decreasing function. Hence we introduce a negative sign and write η

_{d}= -p . dx

^{2}. X is the demand for a good at price 'p'. Calculate the elasticity of demand.

^{2}

_{d}= - p . dx = - p . ( -4-2p) = > 4p + 2p

^{2}

^{2 }25 -4p -p

^{2}

_{d}= 4(3) + 2 (3)

^{2}= 12 + 18 = 30 = 7.5

^{2}25 -12-9 4

**7.5**

## Find Elasticity of Supply

_{s}= p . dx

^{2}+ 5

^{2}+ 5

_{s}= p . dx = p . 4p = 4p

^{2}

^{2}+ 5 2p

^{2}+ 5

_{s}= 4 (3)

^{2}

_{ }/ [2(3)

^{2}+ 5] = 36 / 23

**elasticity of supply when p =3 is 36/23 = 1.57**

## Maxmum Profit

^{2}+ 10 x + 5 and cost function is 3x

^{2}+ 6x + 2 is for x units. Find the number of units to be sold at maximum profit.

^{2}+ 10x + 5

^{2}+ 6x + 2

^{2}+ 4x + 3

^{2}p / dx

^{2 }= -2 < 0

^{2}p/dx

^{2}< 0. the profit is maximum. Hence profit is maximum when x = 2

^{2}+ 4(2) + 3 = -4 +12 + 3 = 11

**maximum profit is 2 and the profit is 11**

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