Question

Question # 4

a. Evaluate Lim x →6 x^2 - 36/x^2 + 5x - 6

b. the demand curve of a firm is p = -10q + 5900 and its average cost is A (q) = 2q^2 - 4q + 140 + 845/q. where q is the firm's output produced and sold.

1. derive an expression for the total revenue of the firm

ii. derive an expression for the firm's total profit function

iii. derive an expression for the rate of change of profit function of the firm.

iv. is the rate of change of profit increasing or decreasing when the firm's output level is q = 50?

v. determine the level of output for which the total profit of the firm is maximized

vi. what is the firm's maximum profit.

Answer #1

A firms demand function for a good is given by P = 107-2Q and
their total cost function is given by TC = 200+3Q. (using for 6.1
to 6.4)
6.1 Obtain an expression for total revenue (price X quantity)
in terms of Q
6.2 For what values of Q does the firm breakeven?
6.3 Illustrate the answer to (ii) using sketches of the total
cost function, the total revenue function and the profit
function
6.4 From the graph estimate the...

if the marginal cost of a firm is MC = 9q^2 + 2q +1 and the
marginal revenue MR = 60-q. Given that total cost is 3390 when q
-10
(a) Derive an expression for total cost
(b) Derive the expression for total revenue
(c) Using the results from (a) and (b) find the total profit
function

Find the limits, if exists
1. lim?→−6 ?^2 − ? + 4/6 − ? =
2. lim?→5 2? − 10 /(? − 5)(? + 3) =
3. lim?→−4 ?(?) , ?? ?(?) = { 2? + 5, ? < −1 /13 − ? 2 , ? ≥
−1
4. lim?→∞ 4?^3 − 5 /4?^2 + 3? − 1 =
Part II. Find the derivative of the function.
1. ? = 12?^3 + 2?^2 − ? + 3
2. ?(?) =...

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

Optimization Exercise
1. Fat Cattle Inc. cattle feeders uses the following cost
function:
TC= 8,912 + 1.2 X^2 - .003 X^3
Find the production level (X) that minimizes costs.
2. The Smith Farm's profit is related in the following way to
its output:
Profit= -240 + 8Q - 6Q^2
a. Find the firms output equals 6, what is the marginal
profit?
b. What output will maximize the firms profit?
3. Jones Agriculture Inc. hires a consultant to estimate its
profit...

Monopolistically competitive firm with
a demand of Q = 630 – 3P
a total cost function of C(Q) = 25,000 + 10Q.
1. What is the profit-maximizing output level
2. What is the profit or loss from producing at the optimal
level and charging the optimal price
3. At the optimal price and quantity combination, what is your
firm's marginal revenue
4. If your firm's advertising elasticity is 0.02, what is the
optimal amount for you to advertise

1. What is the slope of 〖y=4x〗^0.5+10x^(2 ) when x=16?
2. What is the slope of y=〖100-6x〗^0.5 when x=6?
3. Given the demand function is q=〖(1200-2p)〗^0.5 What is the
point elasticity of demand when quantity is 30? (hint: you should
write p as a function of q and then take the derivative. Then use
the elasticity formula.
4. Derive the TR and MR functions if q=200-0.4p. If TC=11q^3-
22q^2+30q+20 find the MC function.
5. If a firm faces TR and...

1.
If a firm is producing such that MR<MC, they should
A. release more output
B. release less output
C. stay at this level of output
2. In a perfectly competitive market, the current market price
is $12. Given a total cost function, TC(q) = 36 + 2q^2, how much
quantity should a firm release to market?
A. 3
B. 4
C. 5
D. 6

Second look enterprises (SLE) buys old computers, fixes them up,
and resells them. Its weekly revenue function is R = 70q −
2q2 ,so its marginal revenue is MR = 70 − 4q. Its weekly
cost function is C = 10q + 22, so its marginal cost is
MC = 10 + 2q.
a. Use excel to calculate SLE's revenue, cost, and profit for q=
1 to q = 30 in increments of 1. SLE's manager wants to maximize
profit....

2. You have been hired to do some consulting for Fishy Joe’s, a
profit-maximizing monopolistic competitor selling “popplers”. You
have estimated the firm’s demand, marginal revenue, and marginal
cost curves to be, respectively, P = 100 − 2Q, MR = 100 − 4Q, and
MC = 20 + Q, where quantity Q is measured in servings and prices
are measured in dollars per serving. Currently, the firm is
producing where
• Price = $50/serving
• Average Total Cost = $38/serving...

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