Suppose a firm's short run-run production function is q = 2 *
L0.5 , the firm faces a fixed price of L at PL = 4, and
the firm’s fixed cost is 50.
a. Derive the short-run total cost and total variable cost
functions, and then solve for the marginal cost, average variable
cost, and average total cost functions. Assume the firm is a
marginal price taker at P = 60, solve for the firm’s
profit-maximizing amount of L to...
Question 4
A firm has the short-run production function as follows:
Q = L + 15L2 – 0.5L3,
where Q = total products per period and L = number of workers
employed per period.
4.1) Derive the marginal product of labor (MPL). At
what number of workers (L) does the law of diminishing returns
begin?
MPL = f(L) = __________________________________
Law of diminishing return begins when L
= ___________ workers.
4.2) Derive the average product of labor (APL). Find
the number...
A competitive firm has the following short run cost function T C
= Q 3 − 8Q 2 + 30Q + 5 .
(a) Find marginal cost, average cost, and average variable cost
and sketch them on a graph.
(b) At what range of prices will the firm supply zero output,
i.e. shutdown?
(c) Identify the firms supply curve
(d) At what price would the firm supply exactly 6 units of
output?
(e) Compute the price elasticity of supply at...
Suppose a competitive firm has a short-run cost function: C(q) =
100 + 10q − q^2 + q^3 , where q is the quantity of output.
1. Is this a short-run or a long-run cost function? Explain.
2. Find the firm’s marginal cost function: MC(q).
3. Find the firm’s average variable cost function: AVC(q).
4. Find the output quantity that the firm AVC at the minimum.
Does the MC increasing or decreasing before the quantity. And does
the MC increasing...
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 Y =
x11/2x21/2 . Suppose in
the short run factor 2 is fixed at 400 units. The cost of factor 1
is $2 and the cost of factor 2 is $1. The price of the output is $6
each. What's the maximum profit that the firm can
get in the short run?
1400
3600
1800
2000
suppose the firm is in the long run and can now choose both
inputs freely. What's the...
9. a.
Suppose that a firm’s production function is q=9x^1/2 in the short
run, where there are fixed costs of $1000, and x is the
variable input whose cost is $4000 per unit. What is the total cost
of producing a level of output q? In other words, identify
the total cost function C(q).
b. Write down the
equation for the supply curve.
c. If price is
$1000, how many units will the firm produce? What is the level of...
You are planning to estimate a short- run production function
for your firm, and you have collected the following data on labor
usage (L) and output (Q): Labor usage (L) Output (Q)
3 1
7 2
9 3
11 5
17 8
17 10
20 15
24 18
26 22
28 21
30 23
a. Please key in the data into MS Excel for regression analysis.
Estimate your firm’s short-run production function. Do the
parameter estimates have the appropriate algebraic...
You are planning to estimate a short- run production function
for your firm, and you have collected the following data on labor
usage (L) and output (Q):
Labor usage (L) Output (Q)
3 1
7 2
9 3
11 5
17 8
17 10
22 15
24 18
26 22
28 21
30 20
33 19
34 17
a. Please key in the data into MS Excel for regression analysis.
Estimate your firm’s short-run production function. Do the
parameter estimates...