In: Economics

Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the production function is q = 50K^(1/2)L^(1/2). prices of capital and labor are given as r = 2 and w = 8

a) does the production function display increasing, constant, or decreasing returns to scale? how do you know and what does this mean?

b) draw the isoquants for your firms production function using L for the x axis and K for y. how are the factors K and L?

c) derive the expansion path equation. represent it graphically. how does the expansion path change when r = 1 and w = 8?

d) find the total cost function as a function of quantity

e) represent the firms cost minimizing choice of factors to produce a given quantity q in a diagram. if q = 1000, calculate K and L

There is a firm who manufacturers and uses capital (K) and labor
(L) to product output Q such that Q=10KL. The unit price for K and
L are w = $15 and r = $5, respectively.
1).Does the firm’s production exhibit decreasing, constant, or
increasing returns to scale?
2)What is the optimal input bundle (K*, L*) to produce 480 unit
of output?
3)Derive the long run cost function.

A competitive firm uses two inputs, capital (?) and labour (?),
to produce one output, (?). The price of capital, ??, is $1 per
unit and the price of labor, ?? , is $1 per unit. The firm operates
in competitive markets for outputs and inputs, so takes the prices
as given. The production function is ?(?, ?) = 3? 0.25? 0.25. The
maximum amount of output produced for a given amount of inputs is ?
= ?(?, ?) units....

A firm produces output using capital (K) and labor (L). Capital
and labor are perfect complements and 1 unit of capital is used
with 2 units of labor to produce 1 unit of output. Draw an example
of an isoquant. If wages and rent are $2 and $3, respectively, what
is the Average Total Cost?
A firm has a production function given by Q=4KL where K, L and Q
denote capital, labor, and output, respectively. The firm wants to
produce...

A firm uses two inputs, labor and capital, to produce a good. To
keep up with the story, let zℓ ≥ 0 denote the units of labor and zk
≥ 0 the units of capital. The firm’s technology is expressed as a
production function f(zℓ, zk) = 20 z1/5 ℓ
z3/5 k . Let w > 0 and r > 0 be the cost of hiring
a unit of labor and a unit of capital, respectively.
(a) Find the technical...

. A firm uses the inputs of fertilizer (sacks), labor and
hothouses to produce roses. Suppose that when the quantity of labor
and hothouses is fixed, the relationship between the quantity of
fertilizer (F) used and the number of roses (TP) produced is given
by the following table.
F TP
APF
MPF
0 0
10 1,100
20 2,200
30
4,800
40 7,600
50 9,800
60
11,600
70
12,200
80
11,800...

Consider an economy that uses two factors of production, capital
(K) and labor (L), to produce two goods, good X and good Y. In the
good X sector, the production function is X = 4KX0.5 + 6LX0.5, so
that in this sector the marginal productivity of capital is MPKX =
2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5.
In the good Y sector, the production function is Y = 2KY0.5 +
4LY0.5, so that in this sector...

A firm discovers that when it uses K units of capital
and L units of labor it is able to
produce q=4K^1/4
L^3/4 units of output.
Continue to assume that capital and labor can be hired at $40
per unit for labor and $10 for capital. In the long run if the firm
produces 600 units of output, how much labor and capital will be
used and what is the LR Total cost of production?

A firm discovers that when it uses K units of capital
and L units of labor it is able to
produce q=4K^1/4
L^3/4 units of output.
a) Calculate the MPL, MPK and MRTS
b) Does the production function (q=4K^1/4 L^3/4) exhibit
constant, increasing or decreasing returns to scale and
why?
c) Suppose that capital costs $10 per unit and labor can
each be hired at $40 per unit and the firm uses 225 units of
capital in the short run....

A firm produces output y using two factors of production
(inputs), labour L and capital K. The firm’s production function is
?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of
capital r = 2 are taken as parameters (fixed) by the firm. a. Show
whether this firm’s technology exhibits decreasing, constant, or
increasing returns to scale. b. Solve the firm’s long run cost
minimization problem (minimize long run costs subject to the output
constraint) to derive this...

Suppose output, Q, is produced by labor, L, and capital, K,
according to the following function: Q = K ½ L½.. Suppose the firm
sells each unit of output in a competitive market for a price P =
$100. Suppose the firm hires each unit of labor in a competitive
market for a wage W = $25. Suppose the firm has to make do for now
with a stock of capital K = 49; moreover, suppose each unit of
capital...

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