Answer to Question #177218 in Economics for REENA

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

(a) We can find the price elasticity of demand as follows:

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

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

(b) We can find the total revenue as follows:

$$TR_0=P_0Q_0=0\cdot600=0,$$ $$TR_1=P_1Q_1=\$1\cdot500=\$500,$$ $$TR_2=P_2Q_2=\$2\cdot400=\$800,$$ $$TR_3=P_3Q_3=\$3\cdot300=\$900,$$ $$TR_4=P_4Q_4=\$4\cdot200=\$800,$$ $$TR_5=P_5Q_5=\$5\cdot100=\$500,$$ $$TR_6=P_6Q_6=\$6\cdot0=0.$$

(c) We can find the marginal revenue as follows:

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

Finally, we get the following table:

(d) The average revenue curve has the downward slope and its corresponding marginal revenue curve lies below it. As we can see from the table, the marginal revenue is lower than the average revenue. Given the demand for his product, the monopolist can increase his sales by lowering the price and the marginal revenue also falls.