A given fall in P will cause a smaller rise in Q so that total revenue P times

A given fall in p will cause a smaller rise in q so

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A given % fall in P will cause a smaller % rise in Q so that total revenue (P times Q) falls.
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A4) Scenario 1 To find optimum price, We use the demand function Quantity = 5024.58 -136.62(Price of oil ) + 117.41(Price of competitor’s products) – 0.2823(Per capita income of consumers) + 7.87 (Promotional Expenditure of Mustard oil) Total Revenue can be maximized at a point at which there is unit elasticity i.e. PED=1 Total Revenue =P*Q Q= 25521.268 -136.62P ------(1) (Here p is price of the oil, Substituted all values to get this equation) Multiplying P on both sides of equation (1) to get total revenue Total Revenue= 25521.268 P-136.62(P 2 ) First derivative of TR with respect to P d TR/d P = 25521.268 -136.62(2P) We know that when TR is maximum, the slope is zero, hence equalizing the above to zero P=93.40 Hence, Price = 93.40 Competitor’s price =109.14 Income Per Capital= 7620.6015 (after 1% increase) Promotional Expenditure = 1247.31 Total Revenue= Q*P = 12760*93.40 = 1191873.66
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Scenario 2 To find optimum price, We use the demand function Quantity = 5024.58 -136.62(Price of oil ) + 117.41(Price of competitor’s products) – 0.2823(Per capita income of consumers) + 7.87 (Promotional Expenditure of Mustard oil) 6% increase in the competitor’s price Revised competitor’s price = 115.6884 (After 6 % interest) Q=26290.304-136.62 P Revenue is maximized , When Elasticity with respect to price is unity or 1 Therefore, E= slope *(P/Q) 1=136.62 *(P/Q) P=Q / 136.62 ------------(1) Substituting the value of P in the demand equation, 2Q=26290.304 Q=13145.15 Now Substituting Q in Equation 1 P=13145.15/136.62 P=96.21 Total Revenue= Q*P =13145.15*96.21 =1264785.75 Comparing Both the Scenario , We find increase in competitor price benefits Hind Oil as the Net Revenue of its product Increases Total Revenue = 1264785.75 Differential Revenue= 72,912.09 When the competitor increases the price, the company shall benefit if we decrease the price as total revenue increases .
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A5) By considering above table of price , Quantity demanded and total Revenue ,Plotted the demand graph and total revenue graph below: Demand Curve 91.5 92 92.5 93 93.5 94 94.5 95 95.5 96 96.5 97 12400 12600 12800 13000 13200 13400 13600 13800 14000 14200 14400 14600 QUANTITY DEMANDED PRICE Quantity Demanded Total revenue 93.40 12760 1191873 96.21 13145 1264785 Price Quantity Price Quantity
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Total Revenue Curve 1170000 1180000 1190000 1200000 1210000 1220000 1230000 1240000 1250000 1260000 1270000 1280000 12400 12600 12800 13000 13200 13400 13600 13800 14000 14200 14400 14600 TOTAL REVENUE Quantity R e v e n u Quantity Revenue
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