Question

3. Suppose that the cost function of q is given by: C (q) = 16 + 4q + q^2

(a) Find the fixed and variable cost.

(b) Find the average cost and marginal cost. 1

(c) Draw the relationship between MC and AC. Prove that they always intersect at the minimum. (Hint: compute the derivative of AC with respect to q and set it equal to zero. Then use this equation to show that MC=AC)

Answer #1

Ans. 3.

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...

The (total) cost function is given by C = 60 + 80q – 15q2 + 2q3
, where q is the quantity produced by the firm. where, FC(q)=60,
VC(q)=80q – 15q2 +
2q3 , MC(q)=80 – 30q+
6q2and AFC(q)=60/q. 1)Write down the
average variable cost function AVC(q). 2)Write down the average
total cost function AC(q). 3)Find the break-even point (q and AC)
and Find the shut-down point (q and AVC). 4). Draw a graph to
illustrate AC, AVC, and MC...

The demand for product Q is given by Q = 136 -.4P and
the total cost of Q by:
STC = 3000 + 40Q - 5Q^2 + 1/3Q^3
A. Find the price function and then the TR function. See
Assignment 3 or 4 for an example.
B. Write the MR and MC functions below. Remember: MR =
dTR/dQ and MC = dSTC/dQ. See Assignment 5 for a review of
derivatives.
C.What positive value of Q will maximize total
profit? Remember, letting...

5. [Marginal Cost] Find the marginal cost (MC) functions for
each of the following average cost functions.
(a) AC = 2.5Q+4+ 40/Q .
(b) AC = 200/Q +5?6Q+4Q^2 .
(c) AC = 2Q^2 ?8Q+174.

Given information, cost equation C(Q), Marginal cost MC(Q), and
its demand for elasticity equation
Q(p). ?(?) = 0.5?3 − 20?2 + 282.5?
MC(?) = 1.5?2– 40? + 282.50
?d(?) = 16 − (1/20)?
The government decides that the lack of competition in this
market is detrimental to the economy and, for that reason,
government intervention is required. The governor proposes
regulating the price of electricity or nationalizing the power
plant. Do you think the governor is right? [Hint: Is there...

The market demand function for a good is given by Q = D(p) = 800
− 50p. For each firm that produces the good the total cost function
is TC(Q) = 4Q+ Q^2/2 . Recall that this means that the marginal
cost is MC(Q) = 4 + Q. Assume that firms are price takers.
(a) What is the efficient scale of production and the minimum of
average cost for each firm? Hint: Graph the average cost curve
first.
(b) What...

A film studio in Hollywood produces movies according to the
function (yes, they can also produce fractions of movies... Think
of half a movie as a B-movie or so.) q = F(K, L) = K0.5L 0.5
/100.(reads as K to the power of 0.5 times L to the power of 0.5
divided by 100) In the short run, capital (studios, gear) is fixed
at a level of 100. It costs $4,000 to rent a unit of capital and
$1,000 to...

1. Assume that a competitive firm has the total cost function:
TC=1q3−40q2+840q+1800TC=1q3-40q2+840q+1800 Suppose the price of the
firm's output (sold in integer units) is $750 per unit. Using
calculus and formulas to find a solution (don't just build a table
in a spreadsheet as in the previous lesson), what is the total
profit at the optimal integer output level? Please specify your
answer as an integer. Hint 1: The first derivative of the total
cost function, which is cumulative, is...

The (total) cost function is given by C = 60 +
80q – 15q2 + 2q3,
where q is the quantity produced by the firm.
Find the break-even point (q and AC).
Find the shut-down point (q and AVC).
Draw a graph to illustrate AC, AVC, and
MC functions for quantities Q on the interval
between 1 and 10. Make sure you show (put the numbers there) where
exactly the MC curve intercepts AVC and
AC curves.
If the price...

Suppose a competitive firm has as its total cost function:
TC=29+2q2 Suppose the firm's output can be sold (in integer units)
at $77 per unit. Using calculus and formulas (don't just build a
table in a spreadsheet as in the previous lesson), what is the
total profit at the optimal integer output level?
Please specify your answer as an integer. In the case of equal
profit from rounding up and down for a non-integer initial solution
quantity, proceed with the...

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