Question 1. Suppose that a monopoly firm supplies to two different markets with the demand functions: Market 1: q1 = 100 – 2p1 + P2 (1.1) Market 2: q2 = 150 + P1 – 3p2 (1.2) (a) Derive the inverse demand functions for both markets, and explain the relationship between the demand for the two goods. Assume that the firm's cost function is (q, + q2)² .
Question 1. Suppose that a monopoly firm supplies to two different markets with the demand functions: Market 1: q1 = 100 – 2p1 + P2 (1.1) Market 2: q2 = 150 + P1 – 3p2 (1.2) (a) Derive the inverse demand functions for both markets, and explain the relationship between the demand for the two goods. Assume that the firm's cost function is (q, + q2)² .
Chapter1: Making Economics Decisions
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![Question 1.
Suppose that a monopoly firm supplies to two different markets with the demand
functions:
Market 1: q, = 100 – 2p1 +P2
(1.1)
Market 2: q2 = 150 + p1 – 3p2
(1.2)
(a) Derive the inverse demand functions for both markets, and explain the
relationship between the demand for the two goods.
Assume that the firm's cost function is (q1 + 92)².
(b) Derive the profit-maximizing outputs, prices and the maximum profit. Show that it
is true maximum.
(c) Suppose there is a restriction of q2 < 20 in the market for good 2. What is the
impact on the firm's output in both the markets, as well as on the maximum
profit?
Now suppose the firm has a resource constraint such that it can produce a maximum of
40 units of both goods in total, i.e., q, + q2 5 40.
(d) What is the impact on the firm's output in both markets, as well as on the
maximum profit? Compare this result with those in parts (b) and (c) above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e9772df-44c4-4afb-8434-16bf1be59905%2F875b51d5-9fc3-4c7b-9137-da38565dcbc7%2Fsx3udb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 1.
Suppose that a monopoly firm supplies to two different markets with the demand
functions:
Market 1: q, = 100 – 2p1 +P2
(1.1)
Market 2: q2 = 150 + p1 – 3p2
(1.2)
(a) Derive the inverse demand functions for both markets, and explain the
relationship between the demand for the two goods.
Assume that the firm's cost function is (q1 + 92)².
(b) Derive the profit-maximizing outputs, prices and the maximum profit. Show that it
is true maximum.
(c) Suppose there is a restriction of q2 < 20 in the market for good 2. What is the
impact on the firm's output in both the markets, as well as on the maximum
profit?
Now suppose the firm has a resource constraint such that it can produce a maximum of
40 units of both goods in total, i.e., q, + q2 5 40.
(d) What is the impact on the firm's output in both markets, as well as on the
maximum profit? Compare this result with those in parts (b) and (c) above.
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