HUBS 2505 HP Final exam practice Questions And
Answers
the production function is given by F(L) = 6L^2/3. Suppose that the cost per
unit of labor is $8 and the price of output is 4, how many units of labor will the
firm hire?
a.16
b.8
c.4
d.24
e.None of the above.
B
production function
F(L)=6L^2/3
Marginal Product of Labor = dF(L)=dL
MPL = 4L^(-1/3)
to obtain the number of labors hired equate MPL = W/P
4L^(-1/3) = 8/4
4L^(-1/3) = 2
L^(-1/3) = 1/2
L=8
the production function is given by f(x) = 4x^1/2. If the price of the commodity
produced is $100 per unit and the cost of the input is $15 per unit, how much
profit will the firm make if it maximize profits?
a.$2,666.67
b.$1,331.33
c.$5,337.33
d.$2,651.67
e.$1,336.33
A
the production is given as f(x)= 4x^(1/2)
the price of production is $100 per unit and price of input is $15 per unit
the profit function of the firm is as follows
pi= TR-TC
TR is the total revenue that us earned by selling q units at $100 per unit. Thus TR
becomes
400q^1/2
,TC is the total cost of production so TC becomes
15q
to calculate the level of output at which the output is maximized, calculate the first
derivative of the profit function and equate it to zero
pi= 400q^1/2-15q
dpi/dq=((200)/(q^1/2)) - 15
((200)/(q^1/2)) - 15 =0
q=1600/9
thus the output level at which profit maximized is 1600/9 units
substitute this value of q into the profit function
pi= 400q^1/2-15q
400(1600/9)^(1/2) -15 (1600/9)=
2666.67
the production function is f(x1, x2) = x1^(1/2)x2^(1/2). If the price of factor 1 is
$4 and the price of factor 2 is $6, in what proportions should the firm use
factors 1 and 2 if it wants to maximize profits?
a.x1 = x2.
b.x1 = 0.67x2.
c.x1 = 1.50x2.
d.We can't tell without knowing the price of output.
e.x1 = 6x2.
C
f(x1, x2) = (x1x2)^(1/2)
MRS = (MU x1)/(MU x2)= (x2/x1)
MRS= Px1/ Px2
(X2/X1) = 4/6
(X2/X1) = 2/3
x1= 3/2X2 = 1.5X2
when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal
product of fertilizer is 1 − N/200 bushels of corn. If the price of corn is $1 per
bushel and the price of fertilizer is $.40 per pound, then how many pounds of
fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
a.64
b.120
c.248
d.240
e.200
, B
we know in order too maximize profit,
value of Marginal product of fertilizers = marginal cost of fertilizers
thus value of MP of fertilizers = price *MPL
.40= 1(1-N/200)
.40=1-N/200
N/200= .60
N= 120
A competitive firm produces output using three fixed factors and one variable
factor. The firm's short-run production function is q = 305x − 2x^2, where x is
the amount of variable factor used. The price of the output is $2 per unit and
the price of the variable factor is $10 per unit. In the short run, how many units
of x should the firm use?
a.37
b.150
c.21
d.75
e.None of the above.
D
firm's short run production function is
q= 305X - 2x^2
x= variable factor
firms profit function is given by
pi = pq-10x
pi= 2(305X - 2x^2) -10x
pi= 2(305X - 2x^2) -10x
pi = 610x - 4x^2-10x
pi = 600x - 4x^2
dpi/dx= 600-8x
600-8x=0
600=8x
x=75
A firm produces one output using one input. When the cost of the input was $3
and the price of the output was $3, the firm used 6 units of input to produce 18
units of output. Later, when the cost of the input was $7 and the price of the
output was $4, the firm used 5 units of input to produce 20 units of output.
This behavior
a. is consistent with WAPM.
b. is not consistent with WAPM.
c. is impossible no matter what the firm is trying to do.
Answers
the production function is given by F(L) = 6L^2/3. Suppose that the cost per
unit of labor is $8 and the price of output is 4, how many units of labor will the
firm hire?
a.16
b.8
c.4
d.24
e.None of the above.
B
production function
F(L)=6L^2/3
Marginal Product of Labor = dF(L)=dL
MPL = 4L^(-1/3)
to obtain the number of labors hired equate MPL = W/P
4L^(-1/3) = 8/4
4L^(-1/3) = 2
L^(-1/3) = 1/2
L=8
the production function is given by f(x) = 4x^1/2. If the price of the commodity
produced is $100 per unit and the cost of the input is $15 per unit, how much
profit will the firm make if it maximize profits?
a.$2,666.67
b.$1,331.33
c.$5,337.33
d.$2,651.67
e.$1,336.33
A
the production is given as f(x)= 4x^(1/2)
the price of production is $100 per unit and price of input is $15 per unit
the profit function of the firm is as follows
pi= TR-TC
TR is the total revenue that us earned by selling q units at $100 per unit. Thus TR
becomes
400q^1/2
,TC is the total cost of production so TC becomes
15q
to calculate the level of output at which the output is maximized, calculate the first
derivative of the profit function and equate it to zero
pi= 400q^1/2-15q
dpi/dq=((200)/(q^1/2)) - 15
((200)/(q^1/2)) - 15 =0
q=1600/9
thus the output level at which profit maximized is 1600/9 units
substitute this value of q into the profit function
pi= 400q^1/2-15q
400(1600/9)^(1/2) -15 (1600/9)=
2666.67
the production function is f(x1, x2) = x1^(1/2)x2^(1/2). If the price of factor 1 is
$4 and the price of factor 2 is $6, in what proportions should the firm use
factors 1 and 2 if it wants to maximize profits?
a.x1 = x2.
b.x1 = 0.67x2.
c.x1 = 1.50x2.
d.We can't tell without knowing the price of output.
e.x1 = 6x2.
C
f(x1, x2) = (x1x2)^(1/2)
MRS = (MU x1)/(MU x2)= (x2/x1)
MRS= Px1/ Px2
(X2/X1) = 4/6
(X2/X1) = 2/3
x1= 3/2X2 = 1.5X2
when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal
product of fertilizer is 1 − N/200 bushels of corn. If the price of corn is $1 per
bushel and the price of fertilizer is $.40 per pound, then how many pounds of
fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
a.64
b.120
c.248
d.240
e.200
, B
we know in order too maximize profit,
value of Marginal product of fertilizers = marginal cost of fertilizers
thus value of MP of fertilizers = price *MPL
.40= 1(1-N/200)
.40=1-N/200
N/200= .60
N= 120
A competitive firm produces output using three fixed factors and one variable
factor. The firm's short-run production function is q = 305x − 2x^2, where x is
the amount of variable factor used. The price of the output is $2 per unit and
the price of the variable factor is $10 per unit. In the short run, how many units
of x should the firm use?
a.37
b.150
c.21
d.75
e.None of the above.
D
firm's short run production function is
q= 305X - 2x^2
x= variable factor
firms profit function is given by
pi = pq-10x
pi= 2(305X - 2x^2) -10x
pi= 2(305X - 2x^2) -10x
pi = 610x - 4x^2-10x
pi = 600x - 4x^2
dpi/dx= 600-8x
600-8x=0
600=8x
x=75
A firm produces one output using one input. When the cost of the input was $3
and the price of the output was $3, the firm used 6 units of input to produce 18
units of output. Later, when the cost of the input was $7 and the price of the
output was $4, the firm used 5 units of input to produce 20 units of output.
This behavior
a. is consistent with WAPM.
b. is not consistent with WAPM.
c. is impossible no matter what the firm is trying to do.
