Question

3.Find the Total revenue, average revenue and marginal revenue as the total revenue equation is given as;

TR= 100-10Q^2 , from Q=0 to Q=6.

Answer 1

(a) Let's calculate the TR function for each quantity:

$$TR_0=100-10\cdot0^2=\$100,$$ $$TR_1=100-10\cdot1^2=\$90,$$ $$TR_2=100-10\cdot2^2=\$60,$$ $$TR_3=100-10\cdot3^2=\$10,$$ $$TR_4=100-10\cdot4^2=-\$60,$$ $$TR_5=100-10\cdot5^2=-\$150,$$ $$TR_6=100-10\cdot6^2=-\$260.$$

(b) Then, we can calculate the average revenue for each quantity:

$$AR_1=\dfrac{TR_1}{Q_1}=\dfrac{\$90}{2}=\$45,$$ $$AR_2=\dfrac{TR_2}{Q_2}=\dfrac{\$60}{3}=\$20,$$ $$AR_3=\dfrac{TR_3}{Q_3}=\dfrac{\$10}{3}=\$3.3,$$ $$AR_4=\dfrac{TR_4}{Q_4}=\dfrac{-\$60}{4}=-\$15,$$ $$AR_5=\dfrac{TR_5}{Q_5}=\dfrac{-\$150}{5}=-\$30,$$ $$AR_6=\dfrac{TR_6}{Q_6}=\dfrac{-\$260}{6}=-\$45.3.$$

c) In order to find MR we need to take derivative of TR with respect to Q:

$$MR=\dfrac{dTR}{dQ}=-20Q.$$

Let's calculate MR for each quantity:

$$MR_1=\dfrac{TR_1-TR_0}{Q_1-Q_0}=\dfrac{\$90-\$100}{1-0}=-\$10,$$ $$MR_2=\dfrac{TR_2-TR_1}{Q_2-Q_1}=\dfrac{\$60-\$90}{2-1}=-\$30,$$ $$MR_3=\dfrac{TR_3-TR_2}{Q_3-Q_2}=\dfrac{\$10-\$60}{3-2}=-\$50,$$ $$MR_4=\dfrac{TR_4-TR_3}{Q_4-Q_3}=\dfrac{-\$60-\$10}{4-3}=-\$70,$$ $$MR_5=\dfrac{TR_5-TR_4}{Q_5-Q_4}=\dfrac{-\$150-(-\$60)}{5-4}=-\$90,$$ $$MR_6=\dfrac{TR_6-TR_5}{Q_6-Q_5}=\dfrac{-\$260-(-\$150)}{6-5}=-\$110.$$