3
of 3
y2
4: A Örmís production function is given by:
K2
Q = 2KL
L2
(8)
where Q is output, L is hours of work and K is use of machinery and equipment.
(a) Find the total di§erential, dQ
(b) Set dQ = 0 and Önd
dK :
dL
5: We have the following function
z=
x3
24
4y2 + 12xy + 20x
2y
(9)
(a) Find the stationary values. that is, Önd the values of x and y that solve the Örst order conditions.
(b) Consider each stationary value. Determine if it is a minimum, maximum or a saddle point.
6:A monopolist produces an identical product in 2 plants. The cost of production in the Örst plant
is given by
C1 = Q1 + 0:5Q21
(10)
where Q1 is output produced in the Örst plant. The cost of production in the second plant is:
C2 = 2Q22
Q2
(11)
where Q2 is output produced in the second plant. The total demand for the Örmís product is given by:
P = 100
2QT
(12)
QT = Q1 + Q2
(13)
where QT is total output produced
The cost of production in the Örst plant is given by:
T C = C1 + C2
(14)
The total demand for the Örmís product is given by:
P = 500
2QT
(15)
QT = Q1 + Q2
(16)
where
2
:
https://brightspace.carleton.ca/d2l/le/content/208403/viewContent/3470943/View
2023-11-07, 3 10 PM
Page 1 of 1