Question

  From the give table calculate Elasticity of Price, Total Revenue and Marginal Revenue. Also, explain the relationship between AR and MR?

Price Quantity Total Revenue Marginal Revenue

6 0

5 100

4 200

3 300

2 400

1 500

0 600 

Answer 1

Solution for finding Elasticity of Price.

$$E_d=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{\dfrac{P_2-P_1}{0.5(P_2+P_1)}},$$

$​ ​ ​$

$$E_d=\dfrac{\dfrac{100-500}{0.5(100+500)}}{\dfrac{5-1}{0.5(5+1)}}=-1.0$$

​Price elasticity will be -1.0.

The solution on how to find the total revenue will be as follows

$$TR_0=P_0Q_0=0\times600=0,$$ $$TR_1=P_1Q_1=\$1\times500=\$500,$$ $$TR_2=P_2Q_2=\$2\times400=\$800,$$ $$TR_3=P_3Q_3=\$3\times300=\$900,$$ $$TR_4=P_4Q_4=\$4\times200=\$800,$$ $$TR_5=P_5Q_5=\$5\times100=\$500,$$ $$TR_6=P_6Q_6=\$6\times0=0.$$

Marginal revenue.

$$MR_1=\dfrac{TR_1-TR_0}{Q_1-Q_0}=\dfrac{\$500-0}{500-600}=-\$5,$$ $$MR_2=\dfrac{TR_2-TR_1}{Q_2-Q_1}=\dfrac{\$800-\$500}{400-500}=-\$3,$$ $$MR_3=\dfrac{TR_3-TR_2}{Q_3-Q_2}=\dfrac{\$900-\$800}{300-400}=-\$1,$$ $$MR_4=\dfrac{TR_4-TR_3}{Q_4-Q_3}=\dfrac{\$800-\$900}{200-300}=\$1,$$ $$MR_5=\dfrac{TR_5-TR_4}{Q_5-Q_4}=\dfrac{\$500-\$800}{100-200}=\$3,$$ $$MR_6=\dfrac{TR_6-TR_5}{Q_6-Q_5}=\dfrac{0-\$500}{0-100}=\$5.$$

From the above information, we get the following table.

Relationship between AR and MR.

The average revenue curve is sloped downward, and the marginal revenue curve is sloped downward as well. The marginal revenue is smaller than the average revenue, as seen in the table. Given the market for his product, the monopolist will boost profits by lowering the price, while marginal revenue declines.