# 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.

Update:

Rating

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