3 trang 1 lượt tải

Microeconomic Homework 9 Analysis and Solutions | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

2

What is price and optimal quantity that gives the firm maximum profit? Using Lerner indicator (L) to identify market power of this firm? ➢ Demand function is 𝑃 = 15 − 𝑄 (1) so the marginal revenue function is 𝑀𝑅 = 15 − 2𝑄 (2). ➢ The total cost function is 𝑇𝐶 = 7𝑄 so the marginal cost function is 𝑀𝐶 = 7. ➢ The firm maximum profit when 𝑀𝑅 = 𝑀𝐶. Tài liệu được sưu tầm và soạn thảo dưới dạng file PDF để gửi tới các bạn cùng tham khảo, ôn tập đầy đủ kiến thức, chuẩn bị cho các buổi học thật tốt. Mời bạn đọc đón xem!

Môn: Microeconomics 635 tài liệu

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh 1.9 K tài liệu

Tác giả:

Profile

Mai Nguyệt

2 ngày trước
Tải xuống
Báo cáo
Danh sách Quiz
Tải xuống
/3
Microeconomic homework 9
Problem 1:
Problem 1:
Problem 1:
Problem 1: Problem 1:
a. What is price and optimal quantity that gives the firm maximum profit? Using Lerner
indicator (L) to identify market power of this firm?
➢ Demand function is so the marginal revenue function is 𝑃 = 15 − 𝑄 (1) 𝑀𝑅 = 15 − 2𝑄
(2).
➢ The total cost function is so the marginal cost function is . 𝑇𝐶 = 7𝑄 𝑀𝐶 = 7
➢ The firm maximum profit when so . 𝑀𝑅 = 𝑀𝐶 15 − 2𝑄 = 7
➢ Replacing Q in (1) by 4, we have the optimal price is 9 dollars.
➢
Using the Lerner indicator we have market power for this firm is: L =
P−MC
P
=
9−7
9
=
2
9
b. What is price and optimal quantity for society (for perfect competitive market)? Identify dead-
weight loss (DL) created by this firm?
➢ The price and optimal quantity for society are at the point that D = MC so 15 − Q = 7
➢ Solving the equation, we have optimal quantity for society is 8 units.
➢ Replacing Q in (1) by 8, we have the optimal price for society 7 dollars.is
The ad weight lost is S so
de
AEB
𝐷𝑊𝐿 =
(9−7)(8−4)
2
= 4
MC
P
Q
9
A
B
E
7
4
8
Problem 2
Problem 2
Problem 2
Problem 2 Problem 2
a. What optimal output level that maximizes profit? What is that maximum profit? is
Demand function is so marginal revenue function is . 𝑃 = 100 − 𝑄 𝑃 = 100 − 2𝑄
Total cost function is
TC = Q. AVC + FC = Q
2
+ +4Q 200 so the marginal cost function is
MC = TC' = 2Q + 4.
To maximize profit MR = MC so 100 − 2Q = 2Q + 4.
Solving the equation, we have the optimal quantity for the firm 2is 7 units.
Replacing Q in demand function we have optimal price for the firm is 73 dollars.
b. What is consumer surplus (CS) and deadweight loss (DL) created by this firm?
𝐶𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 = 𝐼𝐴𝑃’ =
( ).100 73− 27
2
= 364.5
𝐷𝑒𝑎𝑑𝑤𝑒𝑖𝑔ℎ𝑡 𝑙𝑜𝑠𝑠 = 𝐸𝐴𝐵 =
(32 27− ). (73 46− )
2
= 67.5
c. Assume this firm applies perfect price discrimination, what is quantity and variable profit of
the firm?
If the firm applies perfect price discrimination, we have optimal quantity at 𝑀C = D so optimal quantity
is 32 units optimal price is 68 dollar and s.
Variable profit for the firm is producer surplus:
PS = IED =
(100 32−4).
2
= 1536
MC
P
Q
P’
A
B
E
D
Q’
I
P
1
d. Identify relationship between variable profit (PS) that the firm gets before and after applying
perfect price discrimination and consumer surplus and deadweight loss ?
The relationship between variable profit for the firm applying price discrimination and consumer
surplus and deadweight loss is: VP = PS + CS + DWL

Tài liệu khác của Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

Preview text:

Microeconomic homework 9 Pr P o r b o l b e l m e m 1 : 1 :
a. What is price and optimal quantity that gives the firm maximum profit? Using Lerner
indicator (L) to identify market power of this firm?
➢ Demand function is 𝑃 = 15 − 𝑄 (1) so the marginal revenue function is 𝑀𝑅 = 15 − 2𝑄 (2).
➢ The total cost function is 𝑇𝐶 = 7𝑄 so the marginal cost function is 𝑀𝐶 = 7.
➢ The firm maximum profit when 𝑀𝑅 = 𝑀𝐶 so 15 − 2𝑄 = 7.
➢ Solve the equation we have optimal quantity is 4 units.
➢ Replacing Q in (1) by 4, we have the optimal price is 9 dollars.
➢ Using the Lerner indicator we have market power for this firm is: L = P−MC = 9−7 = 2 P 9 9
b. What is price and optimal quantity for society (for perfect competitive market)? Identify dead-
weight loss (DL) created by this firm?
➢ The price and optimal quantity for society are at the point that D = MC so 15 − Q = 7
➢ Solving the equation, we have optimal quantity for society is 8 units.
➢ Replacing Q in (1) by 8, we have the optimal price for society is 7 dollars. P 9 A B MC 7 E 4 8 Q The d a
e d weight lost is SAEB so 𝐷𝑊𝐿 = (9−7)(8−4) = 4 2 Pr P o r b o l b e l m e m 2 2
a. What is optimal output level that maximizes profit? What is that maximum profit?
Demand function is 𝑃 = 100 − 𝑄 so marginal revenue function is 𝑃 = 100 − 2𝑄.
Total cost function is TC = Q. AVC + FC = Q2 + 4Q + 200 so the marginal cost function is MC = TC' = 2Q + 4.
To maximize profit MR = MC so 100 − 2Q = 2Q + 4.
Solving the equation, we have the optimal quantity for the firm is 27 units.
Replacing Q in demand function we have optimal price for the firm is 73 dollars.
b. What is consumer surplus (CS) and deadweight loss (DL) created by this firm? P MC I P’ A P1 B E D Q’ Q (100 − 73).27
𝐶𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 = 𝐼𝐴𝑃’ = = 364.5 2 (32 − 27). (73 − 46)
𝐷𝑒𝑎𝑑𝑤𝑒𝑖𝑔ℎ𝑡 𝑙𝑜𝑠𝑠 = 𝐸𝐴𝐵 = = 67.5 2
c. Assume this firm applies perfect price discrimination, what is quantity and variable profit of the firm?
If the firm applies perfect price discrimination, we have optimal quantity at 𝑀C = D so optimal quantity
is 32 units and optimal price is 68 dollars.
Variable profit for the firm is producer surplus: PS = IED = (100−4).32 = 1536 2
d. Identify relationship between variable profit (PS) that the firm gets before and after applying
perfect price discrimination and consumer surplus and deadweight loss ?
The relationship between variable profit for the firm applying price discrimination and consumer
surplus and deadweight loss is: VP = PS + CS + DWL

Tài liệu liên quan: