Answer to Question #177255 in Microeconomics for AMIT VIKAS MALKAR

Question

1. 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) price elasticity;

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

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

(b) Total revenue;

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

(c) Marginal revenue;

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

d) As AR falls, MR should fall faster than AR. As a result, the MR curve slopes downward, while the AR curve slopes upward (a situation of monopoly and monopolistic competition)

The average revenue curve has the downward slope and its corresponding marginal revenue curve lies below it.

ii) MR equals AR if AR is constant. Both are shown by the same horizontal straight line (perfect competition)

iii) MR but not AR may be negative. This is because MR is limited to one unit and AR is derived by all units. If AR is not constant, it will not equal MR and will also have an effect on MR's ideal conditions.