Question
In: Economics
The production function of a firm is given as Q = 50√KL. Here Q is the...
The production function of a firm is given as Q = 50√KL. Here Q is the output produced, K is the capital input and L is the labor input.
Take the partial derivative of the long-term cost function according to the wage, interpret the function you find. Do the same for the rent cost of the capital (take derivative according to r). Interpret the function you find.
Solutions
Rahul Sunny answered 5 months agoRelated Solutions
27) A firm has a production function Q = KL, where Q is the quantity of...
27) A firm has a production function Q = KL, where Q is the
quantity of output, K is the amount of capital and L is the amount
of labor. MPL=K and MPK=L.
a) Suppose that capital is fixed at K=10 in short run. In this
case, the marginal product of labor is MPL=10. Does this production
function exhibit diminishing marginal returns to labor?
b) Suppose that in the short run, K is fixed at 10. The interest
rate is...
A firm has a production function Q = KL, where Q is the quantity of output,...
A firm has a production function Q = KL, where Q is the quantity
of output, K is the amount of capital and L is the amount of labor.
MPL=K and MPK=L .
a) Suppose that capital is fixed at K=10 in short run. In this
case, the marginal product of labor is MPL=10. Does this production
function exhibit diminishing marginal returns to labor?
b) Suppose that in the short run, K is fixed at 10. The interest
rate is...
A firm has a production function of Q = KL + L, where MPL = K...
A firm has a production function of Q = KL +
L, where MPL = K + 1 and
MPK = L. The wage rate (W) is
$100 per worker and the rental (R) is $100 per unit of
capital.
a. In the short run, capital (K) is fixed at 4 and the
firm produces 100 units of output. What is the firm's total
cost?
b. In the long run, what is the total cost of producing 100
units of...
Suppose the production function for widgets is given by q = kl -0.8k2- 0.2l2, where...
Suppose the production function for widgets is given by
q = kl -0.8k2- 0.2l2,
where q represents the annual quantity
of widgets produced, k represents annual capital input, and l
represents annual labor input.
Suppose k = 10; graph the total and average productivity of
labor curves. At what level of labor input does this average
productivity reach maximum? How many widgets are produced at that
point?
Again, assuming that k = 10, graph the MPL curve. At
what...
Suppose the production function for widgets is given by q = kl -0.8k2- 0.2l2, where...
Suppose the production function for widgets is given by
q = kl -0.8k2- 0.2l2,
where q represents the annual quantity
of widgets produced, k represents annual capital input, and l
represents annual labor input.
Suppose k = 10; graph the total and average productivity of
labor curves. At what level of labor input does this average
productivity reach maximum? How many widgets are produced at that
point?
Again, assuming that k = 10, graph the MPL curve. At
what...
2. Suppose that a firm's production function is given by Q = KL(MPK = L and...
2. Suppose that a firm's production function is given by Q =
KL(MPK = L and MPL = K), where Q is the quantity of output, K is
units of capital, and L is units of labor. The price per unit of
labor and capital are $30 and $20, respectively.
(a) How many units of labor and capital should the firm use if
it wants to minimize the cost of producing 600 units of output?
(b) Suppose that the firm...
A firm has the following production function: q=KL The firm will produce 64 units of output...
A firm has the following production function: q=KL The firm will
produce 64 units of output and faces prices for labor and capital
of $4 and $1 respectively. What is the optimal quantity of labor
and capital the firm should employ in order to minimize the cost of
producing 64 units of output? What is the minimum cost of producing
64 units of output? Show the firms optimal production decision on a
graph.
Short Run Cost Curves: Consider a firm with the following production function: q=(KL)/20 a. For a...
Short Run Cost Curves: Consider a firm with the following
production function: q=(KL)/20 a. For a short-run situation in
which K=10, wage = 4 and cost of capital = 1, derive expressions
for short run total cost and short run average cost for this
production function. b. Plot the short-run total cost curve and
label it “TC1”. Now suppose that the cost of capital goes up to 2.
(Continue to assume we’re in the short run and K can not...
The production function of a firm is given by F(K, L)=KL. Assume that capital (K) is...
The production function of a firm is given by F(K, L)=KL. Assume
that capital (K) is fixed at K=1 in the short run. Then the amount
of labor (L) needed to produce 4 unit of output is equal to
___.
The production function of a firm is given by F(K, L)=KL. Assume that capital (K) is...
The production function of a firm is given by F(K, L)=KL. Assume
that capital (K) is fixed at K=1 in the short run. Then the amount
of labor (L) needed to produce 4 unit of output is equal to ___.
Group of answer choices 16 1 4 8 2
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