Question

Consider the following cost functions.

**
i.** *LTC*(*q*) =
3*q*^{3} – 6*q*^{2},

** ii.**
*STC*(*q*) = 8*q*^{2} + 800.

For each function, answer the following

** a.** What
is its total variable cost and total fixed cost?

** b.** At
what output is average cost minimized?

** c.**
Graph the marginal and average cost curves.

Answer #1

*LTC*(*q*) = 3*q*^{3} –
6*q*^{2}, ATC = TC/q = 3q^2 - 6q

also MC = dTC/dq = 9q^2 - 12q

all of this is total variable cost as there is no constant term to indicate fixed costs of production

so TVC = 3*q*^{3} – 6*q*^{2} and
TFC = 0

Average cost is minimized at dATC/dq = 0

= 6q - 6 = 0

6q = 6 or q = 1, the average total costs are minimized at q=1

*STC*(*q*) = 8*q*^{2} + 800, ATC =
TC/q = 8q + 800/q

also MC = dTC/dq = 16q

so TVC = 8*q ^{2}* and TFC = 800

Average cost is minimized at dATC/dq = 0

= 8-800/q^2 = 0

800/q^2 = 8

q^2 = 100

q = +-10, negative value ignored, so q = 10

, the average total costs are minimized at q=10

Use the following long run total cost (LTC) function to answer
the question that follows, LTC=Q^3 - 100Q^2 + 2550Q
a. What levels of output will this firm experience economies of
scale?
i. Q<
b. What levels of output will this firm experience diseconomies
of scale?
ii. Q>

a) A firm's long-run total cost function is given by
LTC = 115,000 Q – 500 Q 2 +
Q 3, where long-run marginal cost is given by
LMC = 115,000 – 1,000 Q + 3 Q
2. At what range of output does this firm have economies
of scale?

Consider the cost function C= 40 + 3Q 2Q^2 + 1/2Q^3 . i) At Q =
4, what is the firm’s average fixed cost? ii) At Q = 4, what is the
firm’s marginal cost? iii) If the firm optimally produces Q = 4,
and P = 35-aQ, what does a have to be? iv) Which Q minimizes the
firm’s average variable cost? v) What is the firm’s minimum average
variable cost?99

1. Consider the following short- run variable cost function for
a firm.
VC = q3 - 10q2 + 100q
a. Find the equation for the short-run average variable cost and
marginal cost.
b. Using your answer to part a, show that the output label at which
short-run average variable cost is minimized is greater than the
output level at which short-run marginal cost is minimized.
c. Using your answers to part (a) and (b), draw a rough sketch of
the...

A price-taking firm's variable cost function is
VC=3Q3,
where Q is its output per week. It has a sunk fixed cost
of $750 per week. Its marginal cost is
MC=9Q2.
a. What is the firm’s supply function when the $750 fixed cost is
sunk?
Instructions: Enter your
answer as a whole number.
Q =
(P/9)0.5 for P ≥ $.
b. What is the firm’s supply function when the fixed cost is
avoidable?
Instructions: Enter
your answer as a whole...

A price-taking firm's variable cost function is
VC=3Q3,
where Q is its output per week. It has a sunk fixed cost
of $750 per week. Its marginal cost is
MC=9Q2.
a. What is the firm’s supply function when the $750 fixed cost is
sunk?
Instructions: Enter your
answer as a whole number.
Q =
(P/9)0.5 for P ≥ $.
b. What is the firm’s supply function when the fixed cost is
avoidable?
Instructions: Enter
your answer as a whole...

Suppose that a firm's fixed proportion production function is
given by q = min(2k, 4L), and that the rental rates for capital and
labor are given by v = 1, w = 3.
A) Calculate the firm's long-run total, average, and marginal
cost curves.
B) Graph these curves.
C) Suppose that k is fixed at 10 in the short run. Calculate the
firm's short-run total, average, and marginal cost curves and graph
them.
D) Now suppose in the long run...

3. Cost Tables
(a) Fill in the following table, where TFC = Total Fixed Cost,
TVC = Total Variable Cost, TC = Total Cost, AFC = Average Fixed
Cost, AVC = Average Variable Cost, ATC = Average Total Cost, and MC
= Marginal Cost. Remember the following relationships:
TFC + TV C = TC
AF C = T F C/Q, AV C = T V C/Q, AT C = T C/Q
MC = ∆TC ∆Q
Output (Q)
TFC
TVC
TC...

3) Suppose a firm’s cost function is C(q) = 3q2 (2 squared) +
15.
a. Find variable cost, fixed cost, average cost, average
variable cost, and average fixed cost.(Hint: Marginal cost is given
by MC = 6q.)
b. Find the output that minimizes average cost.
:4) Suppose that a firm’s production function is q = x0.5 in the
short run, where there are fixed costs of $1,000, and x is the
variable input whose cost is $1,000 per unit. What...

Consider the following firm with its demand, production and cost
of production functions:
(1) Demand: Q = 230 – 2.5P + 4*Ps + .5*I, where Ps = 2.5, I =
20.
(2) Inverse demand function [P=f(Q)], holding other factors (Ps
= 2.5 and I =20) constant, is, P=100-.4*Q.
(3) Production: Q = 1.2*L - .004L2 + 4*K - .002K2;
(4) Long Run Total Cost: LRTC = 2.46*Q + .00025*Q2 (Note: there
are no Fixed Costs);
(5) Total Cost: TC =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 43 minutes ago

asked 45 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago