In: Economics

11. Supply and Demand - Application of Simultaneous Equations

(a) Find the equilibrium price and quantity in each of the following markets:

(i) Qd = 6 − 2p, Qs = 3 + p;

(ii) Qd = 10 – 5/2 p, Qs = 3 + p;

(iii) Qd = 1 − p, Qs = 3 + p. Comment on the situation in market (iii).

(b) What would be the effect of a purchase/sales tax of 1 cent per item in (ii) above, if p measures price in cents? Explain your answer.

**Part A.**

(i) Qd = 6 − 2p, Qs = 3 + p;

Equilibrium at Qd=Qs

6-2p=3+p

3p = 3

p=1, Q = 3+1 =4

(ii) Qd = 10 – 5/2 p, Qs = 3 + p;

10-5p/2 = 3+p (equate demand and supply equations)

p+5p/2 = 7

7p/2 = 72 (Simplification)

p = 2, q = 3+2 =5

(iii) Qd = 1 − p, Qs = 3 + p.

1-p = 3+p

2p = -2

p=-1, Q = 3-1 = 2 units (The commodity has a negative price which is only in case of bads like garbage etc for which we or the consumers pay. The price in actual market conditions cannot be negative except in case of bads which are paid for, to get rid off.)

**Part B.**

Qd = 10 – 5/2 p, Qs = 3 + p or p = Q-3, supply equation after tax p = Q-3+1 = Q-2 or Q = p+2;

10 – 5/2 p = p+2

p+5p/2 = 8

7p/2 = 8

**p = 16/7 = 2.2857**

**q = 2.2857+2 = 4.2857**

**The price has increased and quantity at equilibrium has
fallen. Due to the tax imposed on the commodity, both the buyers
and sellers will bear the tax depending on the elasticity of demand
and supply. The tax causes the price paid by buyers to rise and
also creates deadweight loss for the society.**

9. Suppose the
following set of simultaneous equations represents the demand and
supply functions for Beef (B) and Chicken (C) fillets in the
Barbecue market:
For
Beef:
QdB = 82 – 3PB + PC
QsB = -5 + 15 PB
For Chicken:
QdC = 92 + 2PB – 4PC
QsC = -6 + 32PC
Find the equilibrium conditions (price
and quantity) for each product.
10. The Table below shows the
Total Utility (TU) and Marginal Utility (MU) derived...

Consider the following supply and demand equations:
Supply: p = 10 + q
Demand: p = 100 − 2q
Show your work as your respond to the following
questions.1
(a) What is the market equilibrium price and quantity?
(5%)
(b) What is the Total Surplus at equilibrium? (5%)
(c) The government enacts a price ceiling at ¯p = 50. What is
the Total Surplus?
D）Calculate the Consumer Surplus under a price ceiling of ¯p =
20.
(e) What is the...

Consider the following supply and demand equations: Supply: p =
10 + q Demand: p = 100 − 2q Show your work as your respond to the
following questions.
(a) What is the market equilibrium price and quantity?
(b) What is the Total Surplus at equilibrium?
(c) The government enacts a price ceiling at ¯p = 50. What is
the Total Surplus?
(d) Calculate the Consumer Surplus under a price ceiling of ¯p =
20.
(e) What is the Deadweight...

Consider the following supply and demand equations:
Supply: p = 10 + q
Demand: p = 100 − 2q
Show your work as your respond to the following questions.1
(a) What is the market equilibrium price and quantity? (5%)
(b) What is the Total Surplus at equilibrium? (5%)
(c) The government enacts a price ceiling at ¯p = 50. What is
the Total Surplus?
D）Calculate the Consumer Surplus under a price ceiling of ¯p =
20.
(e) What is the...

Consider the following supply and demand equations: Supply: p =
10 + q Demand: p = 100 − 2q Show your work as your respond to the
following questions.
(a) What is the market equilibrium price and quantity?
(b) What is the Total Surplus at equilibrium?
(c) The government enacts a price ceiling at ¯p = 50. What is
the Total Surplus?
(d) Calculate the Consumer Surplus under a price ceiling of ¯p =
20.
(e) What is the Deadweight...

Consider the following supply and demand equations:
Supply: p = 10 +
q
Demand: p = 100 −
2q
Show your work as you respond to the
following questions.
What are the market equilibrium price and quantity?
(5%)
What is the Total Surplus at equilibrium?
(5%)
The government enacts a price ceiling at ¯p =
50. What is the Total Surplus? (5%)
Calculate the Consumer Surplus under a price ceiling of
¯p = 20. (5%)
What is the Deadweight Loss...

For this question, the supply and demand equations are : w
= 10 + 0.2QS for supply and w = 40 –
0.2QD for demand.
Suppose a wealthy businessman, strategically buys all the local
clown firms and becomes the only person in town hiring clowns.
Bozos’ firm has a marginal cost of hiring determined by the
equation: MC = 10 + 0.4Q. Assume there is no minimum wage
in the market.
Determine the number of clowns hired and the wage...

Consider the following demand and supply equations in the
market for labour.
Supply: W = 10 + (1/3)
L
Demand: W = 1,000 −
(2/3) L
Show your work as you respond to the following questions.
What is the market equilibrium wage and quantity?
(5%)
The government implements a minimum wage of W
= 370. What is the Consumer Surplus? (5%)
Calculate the Producer Surplus under a minimum wage of
W = 370. (5%)
Find the Deadweight Loss under a...

Consider the following demand and supply equations in the
market for labour.
Supply: W = 10 + (1/3)L
Demand: W = 1, 000 − (2/3)L
Show your work as you respond to the following
questions.
(a) What is the market equilibrium wage and quantity?
(b) The government implements a minimum wage of W = 370.
What is the Consumer Surplus?
(c) Calculate the Producer Surplus under a minimum wage of W =
370.
(d) Find the Deadweight Loss under a...

Solve the simultaneous equations:a) x + y = 7, 3x - 2y = 11b) 7x - 2y = 1, 3x + 4y = 15

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