Hello! Would love if someone could help me with the following: Suppose the total
ID: 1165952 • Letter: H
Question
Hello! Would love if someone could help me with the following:
Suppose the total cost equation of a firm is:
TC(Q)=5,000+2,000Q?10Q^2+0.25Q^3
where Q is the level of output.
a. What is the firm's total fixed cost?
b. What is the equation for the firm's total variable cost?
c. Calculate the firm's total cost for Q=10.
d. What is the equation for the firm's average total cost?
e. Calculate average total cost for Q=10.
f. What is the equation for the firm's marginal cost?
g. Calculate marginal cost for Q=10.
h. What is the equation for the firm's average variable cost?
i. Calculate average variable cost for Q=10.
j. Calculate average variable cost for Q=20.
k. At what quantity of output is average variable cost minimized?
2. Suppose that a firm's production function is Q=5K^0.5 L^0.5 where Q is units of output, K and L are machine hours and labor hours, respectively. Suppose that the amount of K available to the firm is fixed at 100 machines hours.
a. What is the firm's total product of labor equation?
b. Calculate the Total Product of Labor for L=1 to L=10.
c. Calculate the Average Product of Labor for L=1 to L=10.
d. Calculate the Marginal Product of Labor for L=1 to L=10.
e. Does this production function exhibit diminishing returns to labor?
Thank you again!
Explanation / Answer
Answer a) Firm fixed cost = 5000
Answer b) Total variable cost = 2000Q-10Q2 +0.25Q3
Answer c) Firm total cost for Q= 10 units
Total cost = 5000+2000(10)-10(10)2 +0.25(10)3
Total cost = 25000-1000+250
Total cost =24250
Answer d) Total cost = 5000+2000Q-10Q2+0.25Q3
Average total cost = 5000/Q+2000-10Q+0.25Q2
Answer e) When Q = 10
Average total cost = 5000/10+2000-100+0.25(10)2
Average total cost = 2500-100+25= 2425
Answer f)Firm Marginal cost = 2000-20Q+0.75Q2
Answer g)Firm Marginal cost = 2000-20(10)+0.75(10)2
Firm marginal cost = 2000-200+75 = 1875
Answer h)Firm average variable cost =2000-10Q+0.25Q2
Answer i)Firm average variable cost Q= 10
Average variable cost = 2000-100+0.25*10*10 = 1900+25=1925
Answer j ) At Q= 20
Average variable cost= 2000-10(20)+0.25*20*20
AVC= 2000-200+100= 1900
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.