(. 1.1) , . , .
y(x) -, , , , x - . y(x)/x , . Ay Af ( "average".) , , D y/ D x.
( "marginal") . Mf (x) = y' y. , , .
13. y. .
, , . . , 2,5 , , , 5. , 1,5 , 1,5 , , , . .
14 (). Ex(y)
Ex (y) = limD x 0(D y/y: D x/x) = x/y limD x 0D y/ D x = x/y y'.
15. , y (x) x, | Ex (y) |> 1, y (x) , | Ex (y)| < 1, , | Ex (y)| = 1.
.
1. - , , . u = Ax, v = By, Eu(v) = (dv/du) u/v=(B/A) (dy/dx) (Ax/By) = Ex(y);
2. -
Ey (x) = (dx/dy) (y/x) = 1 /Ex (y).
3. x Ty = (ln y)' = y'/y,
Ex (y) = xTy.
4. () () :
Ex (uv) = Ex (u) +Ex (v), Ex (u/v) = Ex (u) -Ex (v).
5.
Ex (xy) = Ex (x) +Ex (y) = 1 +Ex (y)
, Ex (y)>-1, xy ; Ex (y)<-1, xy . ,
Ex (y/x) = Ex (y) -Ex (x) = Ex (y)-1
16. , 1?
. y(x), x - . y/x.
Ex (y/x) = Ex (y) -Ex (x) = Ex (y)-1.
|
|
Ex(y) = 1, Ex(y/x) = 0. , x , .. y/x = c, y = cx. y' = c. , .
. d=d (p) p.
s (p)
, . d(p) , s (p) p. , d' (p)<0, Ep (d)<0 Ep (s)>0.
:
1. Ep (d)<-1, ;
2. Ep (d)>-1, ;
3. Ep (d) = -1, .
17. d=7-p s=p+1, p - . .
. d=s, 7-p=p+1, p=3.
Ep (d) = p/ (p- 7), Ep (s) = p/ (p+ 1).
p=3 Ep(d) = -0,75, Ep(s) = 0,75. p = 3 , .
2. d=(p+8)/(p+2), s=p+0,5, p - . .
q , R (q)- , C (q)- .
P (q) = R (q) -C (q). | (12) |
, , , , , .. MR (q) = MC (q). , (?) , P' (q) = 0, . q 0, P' (q) = 0 . , P'' (q 0)<0, q 0 P (q). , , , R'' (q)<0, C'' (q)>0, .
18.
R (q) = 100 q-q 2, C (q) = q 3-37 q 2+169 q+ 4000.
P (q) = -q 3+36 q 2-69 q- 4000. P' (q) = -3 q 2+72 q- 69=0,
q 2-24 q+ 23=0. q 1 = 1, q 2 = 23.
P'' (q) = -6 q+ 72, P'' (1) = 66, P'' (23) = -66<0,
, q = 23 P max = 1290.