Applied Mathematics for Business and Economics

Lecture Note Differentiation

36 The problem is the same as that in problem 35 for Cq q( )=++^35 q 162 .eFVIdUc

lMhat;TI 35 cMeBaHGnuKmn_Cq q()=++^35 q 162.

37 Su ue in dollars from the sale of q units of a certain

arginal

uløaBIkarlk;TMnijmYyRb cMnYnqÉktakMNt;eday

8. k> etIbrimaNénkarlk;esμInwgb:unμanÉkta eTIbGnuKmn_cMNUl

cMNUl

38

ppose the total reven

commodity is Rq()=− + − 268128 q^2 q

a. At what level of sales is the average revenue per unit equal to the m

revenue?

b. Verify that the average revenue is increasing if the level of sales is less

than the level in part a. and decreasing if the level of sales is greater than

the level in part a.

]bmafacMNUlsrubKitCad ePT

Rq()=− + − 26812 q^2 q

kñúg1ÉktaesμIeTAnwg m:aCIn? x>cUrepÞógpÞat;faGnuKmn_cMNUlmFümekInebIkMriténkarlk;tUc

CagkMritEdl)anrkeXIjkñúgsMNYr k> ehIyfaGnuKmn_cMNUlmFümcuH ebI kMriténkarlk;FM Cag

kMritEdl)anrkeXIjkñúgsMNYr k>.

Assume that total national consumption is given by a function Cx( )where x is

the total national income. The derivative Cx′( )is called the marg

propensity to consume, and if SxC

inal

= − represents total national savings, then

Sx′( )is called the marginal propensity to save. Suppose the consumption

function is Cx( )=+ +80.8 0.8x x. Find the marginal prpensity to consume and

determine the value of x that results in the smallest total savings.

Suppose that the demand equa
39 tion for a certain commodity is qp=−60 0.1 (for

0600 ≤≤p ).

a. Express the elasticity of demand as a function of p.

b. Calculate the elasticity of demand when the price isp= 200. Inte

answer.

At what price is the elasticity of demand equal toെ1?

]bmafasamIk kMNt;edayqp60 0.1

rpret the

c.

artRmUvkarmuxTMnijmYyRbePT = − ¬cMeBaH 0600 ≤≤p ¦.

k> cUrsresrkenSameGLasÞicéntRmUvkarCaGnuKmn_nwgp. x>KNnaeGLasÞicéntRmUvkarenAeBl

RmUvkaresμI-1?

40 Sup is

.

Edléføp= 200 rYcbkRsaycemøIy. K> etIéfø esμIb:unμaneTIbeGLasÞicént

po (for

p≤ 10 ).

se that the demand equation for a certain commodity qp=−200 2^2

0 ≤

a. Express the elasticity of demand as a function of p

b. Calculate the elasticity of demand when the price isp= 6. I

answer.

nterpret the

c. At what price is the elasticity of demand equal toെ1?