Assume there are markets for three goods (Qå denotes demand for good i, Q denotes upply of good i) with interconnected demands and supply. Demand is given for every good by: 1 Qa:=a – 2P –P2 + 2P3, 5 1 Qa :=30 – P2 – P +Ps, 1 Qå:=100 – 2P3 + P1 + P2. upply is given for every good by: 1 1 Q :=10 +P +P – P3, 5 2 5 1 Q :=2P, -P + P3, 1 Q :=5+ P3 + P - P. a) Compute price elasticities ɛq P1, EQ?,P2; €Q%,P3» EQqP3» €Q%P3•

Microeconomics
13th Edition
ISBN:9781337617406
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter6: Elasticity
Section: Chapter Questions
Problem 10QP
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1. Assume there are markets for three goods (Q, denotes demand for good i, Q', denotes
supply of good i) with interconnected demands and supply.
Demand is given for every good by:
Qa:=a – 2P
P2 + 2P3,
2
Qå :=30 – P2
Q:=100 – 2P3 + P1 + ÷P2.
Supply is given for every good by:
1
1
Q: :=10 +P +P2 – P3,
2
1
Q :=2P, -P +P3,
1
1
Q :=5 + P3 + P
P2.
(a)
Compute price elasticities ɛq P1 ; EQ%,P2; €Q%,P3; EQP3» EQ%.P3•
Evaluate these elasticities at a point P = 1, P2 = ,, P3 = 1. What can
(b)
you say about the sign and magnitude of them (elastic/inelastic).
(c)
of equilibrium conditions in the form AP = d, specify A, P, d.
Write down equilibrium conditions for every market. Express the system
(d)
a for all prices to be non-negative?
Find equilibrium prices Pf, P, P. What are conditions on parameter
Transcribed Image Text:1. Assume there are markets for three goods (Q, denotes demand for good i, Q', denotes supply of good i) with interconnected demands and supply. Demand is given for every good by: Qa:=a – 2P P2 + 2P3, 2 Qå :=30 – P2 Q:=100 – 2P3 + P1 + ÷P2. Supply is given for every good by: 1 1 Q: :=10 +P +P2 – P3, 2 1 Q :=2P, -P +P3, 1 1 Q :=5 + P3 + P P2. (a) Compute price elasticities ɛq P1 ; EQ%,P2; €Q%,P3; EQP3» EQ%.P3• Evaluate these elasticities at a point P = 1, P2 = ,, P3 = 1. What can (b) you say about the sign and magnitude of them (elastic/inelastic). (c) of equilibrium conditions in the form AP = d, specify A, P, d. Write down equilibrium conditions for every market. Express the system (d) a for all prices to be non-negative? Find equilibrium prices Pf, P, P. What are conditions on parameter
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