Question

D1 D2 P2 01 02 1. The good illustrated in the graph above has an initial price of $95 per unit. As demand increases from 10,000 units to 11,000 units, price increases to $100 per unit. Calculate the price elasticity of demand. Calculate the change in revenue to the producer. Suppose the price changed from S95 to S195 per unit with the same increase in demand. Calculate the price elasticity. Using the above example, explain what price elasticity means. What demand elasticity value maximizes suppliers' revenues? a. b. c. d. e.

Answer 1

Price Elasticity of demand can be calculated using the following formula

$\large e = \frac{\% \triangle Q}{\% \triangle P}$

$\large e = \frac{\frac{Q_2- Q_1}{\frac{Q_1+Q_2}{2}}}{\frac{P_2-P_1}{\frac{P_1+P_2}{2}}}$

A. Given Q1 = 10,000, Q2 = 11,000

P1 = $ 95, P2 = $ 100

$\large e = \frac{\frac{11000- 10000}{\frac{11000+10000}{2}}}{\frac{100-95}{\frac{100+95}{2}}}$

$\large e = \frac{\frac{1000}{10500}}{\frac{5}{97.5}}$

$\large e = \frac{1000*97.5}{5*10500}$

Elasticity of demand = 1.8571

Generally elasticity is Negative but here it is a positive number since the demand curve has shifted to its right, that is demand has increased.

B. TR1 = P1*Q1 = $95*10000 = $ 950,000

TR2 = P2Q2 = $ 100*11000 = $ 1,100,000

Change in TR = TR2 - TR1 = $ 1,100,000 - $ 950,000

Change in TR = $ 150,000

C. P1 = $ 95, P2 = $ 195

$\LARGE e = \frac{\frac{11000- 10000}{\frac{11000+10000}{2}}}{\frac{195-95}{\frac{195+95}{2}}}$

$\LARGE e = \frac{\frac{1000}{10500}}{\frac{100}{145}}$

$\large e = \frac{1000*145}{10500*100}$

Elasticity of demand = 0.138095

Elasticity of demand = 0.14

D. By price elasticity of demand we mean percent change in quantity due to change on price.

For example in above case elasticity of demand is 0.14 thus it means when 1% of price is increased then the quantity will increase by 0.14%.

For every 1% Change in price the quantity will increase by 0.14%.

E. The suppliers will be able to maximize their revenue when elasticity of demand is unitary elastic.

That is when elasticity of demand = 1

Total Revenue is maximum.

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