1. Chapter 3: Simultaneous Equations
Essential Mathematics for Economics and Business, 4th Edition
Chapter 3: Simultaneous Equations
Worked Example 3.7
© John Wiley and Sons 2013
© John Wiley and Sons 2013

2. Essential Mathematics for Economics and Business, 4th Edition
Worked Example 3.7, Figure 3.5 Equilibrium in the goods market algebraically Equilibrium in the goods market graphically
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3. Worked Example 3.7 Calculate the equilibrium price and quantity
Essential Mathematics for Economics and Business, 4th Edition
Worked Example 3.7 Calculate the equilibrium price and quantity
Demand function: P = Q …(1) and Supply function: P = Q …(2)
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4. Equilibrium in the Goods Market
Essential Mathematics for Economics and Business, 4th Edition
Equilibrium in the Goods Market
when
Qd = Qs and Pd = Ps
Quantity demanded by consumers =
Quantity supplied
Price paid by consumers =
Price suppliers are willing to accept
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5. Find the equilibrium price and quantity algebraically
Essential Mathematics for Economics and Business, 4th Edition
Find the equilibrium price and quantity algebraically
Demand: Pd = Qd Supply: Ps = Qs Equate prices Pd = Ps 100 – 0.5Q = Q 100 – 10 = 0.5Q + 0.5Q …rearranging to solve for Q 90 = Q ….this is the equilibrium quantity Next solve for P, the equilibrium price
At equilibrium:
Qd = Qs
Pd = Ps
In this example it is easier to equate prices, because
the demand and supply functions are given in the form P = f(Q)
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6. Market Equilibrium Pe = 55 Qe = 90
Essential Mathematics for Economics and Business, 4th Edition
Market Equilibrium
Now we know the equilibrium quantity Substitute Q = 90 into either (1) or (2) and solve for Q P = Q …(1) Demand function P = (90) = = 55
Qe = 90
Equilibrium
Q = 90
P = 55
Pe = 55
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7. Find the equilibrium price and quantity graphically. Method Overview:
Essential Mathematics for Economics and Business, 4th Edition
Find the equilibrium price and quantity graphically. Method Overview:
1. Graph the demand function: P = Q 2. Graph the supply function: P = Q 3. Read off the point of intersection Pe
Q e
Demand
Market equilibrium E P Q
Supply
Goods market equilibrium
© John Wiley and Sons 2013

8. Graph the demand function: P = 100 - 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the demand function: P = Q
The demand function: P = Q Vertical intercept at P = 100 : Plot this point P
100 Q
Figure 3.5 Goods market equilibrium
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9. Graph the demand function: P = 100 - 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the demand function: P = Q
The graph cuts the horizontal axis at P = 0. Horizontal intercept, Q =
= 200.
Plot this point P
100 Q
200
Figure 3.5 Goods market equilibrium
© John Wiley and Sons 2013

10. Graph the demand function: P = 100 - 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the demand function: P = Q
Join the vertical intercept P = 100 and the horizontal intercept Q = 200 P
100
P = Q Q
200
Figure 3.5 Goods market equilibrium
© John Wiley and Sons 2013

11. Graph the supply function: P = 10 + 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the supply function: P = Q
The supply function: P = Q Vertical intercept P = 10: Plot this point P
100 10 P = Q Q
200
Figure 3.5 Goods market equilibrium
© John Wiley and Sons 2013

12. Graph the supply function: P = 10 + 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the supply function: P = Q
Horizontal intercept at Q =
= -20
Plot this point P
100 10 P = Q Q
200
Figure 3.5 Goods market equilibrium
- 20
© John Wiley and Sons 2013

13. Graph the supply function: P = 10 + 0.5Q
Essential Mathematics for Economics and Business, 4th Edition
Graph the supply function: P = Q
Join the horizontal intercept Q = -20 and the vertical intercept P = 10. Extend the line as required P
100
P = Q 10 P = Q Q
200
Figure 3.5 Goods market equilibrium
- 20
© John Wiley and Sons 2013

14. Essential Mathematics for Economics and Business, 4th Edition
Equilibrium
Record the value of P at the point of intersection Record the value of Q at the point of intersection
At equilibrium:
Qd = Qs
Pd = Ps P
100
P = Q
P = 55
P = Q 10 Q
- 20
Q = 90
200
Figure 3.5 Goods market equilibrium
© John Wiley and Sons 2013

15. Equilibrium at P = 55, Q = 90 Figure 3.5 Goods market equilibrium P
Essential Mathematics for Economics and Business, 4th Edition
Equilibrium at P = 55, Q = 90 P
100 P = Q 55
Market equilibrium P = Q 10 Q 90
200
Figure 3.5 Goods market equilibrium
© John Wiley and Sons 2013