? asked in 科學數學 · 1 decade ago

數學題 求邊際收入 , 需求彈性

1. a demand function p = D(x) expresses price as a function of the number of items produced and sold. Find the marginal revenue.

(1) p = (1000 / 根號x) + 8

2. given the demand function Q = D(p) = 100 - 2p ( 0 < p < 50 ) ]

(1) find the elasticity of demand. (2) find the elasticity of revenue. (3) determine the range of prices corresponding to elastic, inelastic, or unitary demand.

教教我怎樣去做ar

Update:

我不明白第一題的計算過程

1 Answer

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  • 1 decade ago
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    1. Revenue funtion R(x)=x*p=x(8+1000/√x )= 8x +1000√x

    Marginal revenue = R'(x)= 8+500/√x

    2.

    R(p)=Q*p=p(100-2p)=100p-2p^2

    (1) elasticity of demand= Q'(p)*p/Q (有些書定義有負號)

    = - 2p/(100-2p) = - p/(50-p)

    (2) elasticity of revenue= R'(p)*p/R

    = (100- 4p)*p/(100p-2p^2)=(50-2p)/(50-p)

    (3) elastic demand => -p/(50-p) < -1 => 25< p < 50

    inelastic demand=> -p/(50-p) > -1 => 0 < p < 25

    unitary demand=> -p/(50-p) = -1 => p=25

    2008-11-08 17:09:55 補充:

    (1) Revenue R(x)收入=件數*單價=x(件)*p(元)=x*p(x)=x(8+1000/√x)=8x+1000√x

    (2) Marginal of R(x)=R'(x)= 8 + 1000*(1/2)*x^(-1/2)= 8 + 500/√x

    Source(s): me
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