A. The marginal revenuefrom selling x items is 90-0.02x. The revenue from saleof

Question

A. The marginal revenuefrom selling x items is 90-0.02x. The revenue from saleof the first 100 items is $8800. What is the revenuefrom the sale of the first 200 items? B.       The demandfunction for a certain commodity isp(x)=4-1/30x .  Find the consumersurplus when the sales level is 30. A. The marginal revenuefrom selling x items is 90-0.02x. The revenue from saleof the first 100 items is $8800. What is the revenuefrom the sale of the first 200 items? B.       The demandfunction for a certain commodity isp(x)=4-1/30x .  Find the consumersurplus when the sales level is 30. B.       The demandfunction for a certain commodity isp(x)=4-1/30x .  Find the consumersurplus when the sales level is 30.

Explanation / Answer

PART A>>>>   "marginal revenue" meansdR/dx   = 90 - 0.02 x integrate that to get   R = 90 x - 0.01x2 + C , where C is the integration constant we can evaluate C from the given data that for x = 100, R =8800 plug in and solve for C :     8800 =90 (100) - 0.02 (100)2 + C    this gives C = - 100 thus the revenue eqn is    R = 90 x -0.01 x2 - 100 plug in x = 200 to calculate therevenue:     the result is R =17,500 PART B>>>    the "consumer surplus" isdefined as the integral of [ demand function - market price]dx for x = 30 , the price p = 3 so the function being integrated becomes [ 4 -(1/30) x - 3 ]   which is [ 1 - (1/30) x ] dx this integrates as   [ x - x2 / 60 ]evaluated from x = 0 to x = 30 plugging in these limits, we get a consumer surplusof   30 - (30)2 /60  = 15

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