It is given that the firm earns revenue from the sale of two commodities, that is, commodity-X and commodity-Y
Firm earns Rs.30,000 from sale of commodity-X and Rs.70,000 from sale of commodity-Y.
The own price-elasticity demand of commodity-X is -2.5
It implies if there is 1% increase (decrease) in price, the quantity demanded will decrease (increase) by 2.5%
Similarly, the cross price-elasticity of demand between commodity-X and commodity-Y is 1.1
It implies that the commodities are perfect substitutes to each other. A 1% increase (decrease) in price of one commodity leads to 1.1% increase (decrease) in quantity demanded of other commodity.
Following is the formula to calculate the change in revenue due to change in the price of the commodity-X:
"\u0394R = [R_X(1+E_{Q_X, P_X})+R_Y(E_{Q_Y, P_X})](\\% \u0394P_X) \\;\\;(1)"
ΔR is the revenue earned from sale of commodity-X
"E_{Q_X, P_X}" is the own price-elasticity of demand
"R_Y" is the revenue earned from sale of commodity-Y
"E_{Q_Y, P_X}" is the cross price elasticity of demand
"\\% \u0394P_X" is the percentage change in price of commodity-X
The values of the above variables are as follows:
"R_X=30000 \\\\\n\nE_{Q_X, P_X} = -2.5 \\\\\n\nR_Y = 70000 \\\\\n\nE_{Q_Y, P_X} = 1.1 \\\\\n\n\\% \u0394P_X = 1 \\% \\; or \\;0.01"
Substituting these values into equation (1), the change in revenue is as follows:
"\u0394R = [R_X(1+E_{Q_X, P_X})+R_Y(E_{Q_Y, P_X})](\\% \u0394P_X) \\\\\n\n= [30000(1+(-2.5))+(70000)(1.1)](0.01) \\\\\n\n= (-45000+77000)(0.01) \\\\\n\n= 320"
Answer: Rs.320
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