a. Complete the table and determine equilibrium price and quantity. [3.5] b. What will be effect on equilibrium price and quantity when demand and supply functions increase to Qd'x = 120 5Px and…

Model Answer

a. Complete the table and determine equilibrium price and quantity

Given:

• Demand function: $Q_d=100-2P$
• Supply function: $Q_s=20+3P$

Step 1: Find equilibrium price and quantity Equilibrium occurs where $Q_d=Q_s$.

$$100-2P=20+3P$$ $$100-20=3P+2P$$ $$80=5P$$ $$P=16$$

Substitute $P=16$ into either $Q_d$ or $Q_s$:

$$Q=100-2(16)=100-32=68$$

Equilibrium price = 16, Equilibrium quantity = 68

Step 2: Complete the table

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b. Effect on equilibrium price and quantity when demand and supply functions increase

New demand function: $Q_d^{\prime }=120-5P$ New supply function: $Q_s^{\prime }=40+5P$

Step 1: Find new equilibrium price and quantity

$$120-5P=40+5P$$ $$120-40=5P+5P$$ $$80=10P$$ $$P=8$$

Substitute $P=8$ into either $Q_d^{\prime }$ or $Q_s^{\prime }$:

$$Q=120-5(8)=120-40=80$$

New equilibrium price = 8, New equilibrium quantity = 80

Step 2: Compare with original equilibrium

Conclusion:

• Price decreases from 16 to 8.
• Quantity increases from 68 to 80.

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c. Compute price elasticity of demand at both equilibrium prices and compare

Price elasticity of demand (PED) formula:

$$E_d=\frac{dQ}{dP}\times \frac{P}{Q}$$

For original demand function $Q_d=100-2P$:

$$\frac{dQ}{dP}=-2$$

At equilibrium $P=16,Q=68$:

$$E_d=(-2)\times \frac{16}{68}=-0.47$$

For new demand function $Q_d^{\prime }=120-5P$:

$$\frac{dQ}{dP}=-5$$

At equilibrium $P=8,Q=80$:

$$E_d=(-5)\times \frac{8}{80}=-0.5$$

Comparison:

Conclusion:

• Both demand functions are inelastic (|Ed| < 1).
• The new demand is slightly more elastic than the original, but still inelastic.

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# Python code to compute equilibrium and elasticity
def equilibrium(Qd_func, Qs_func):
    # Solve Qd = Qs
    # Example: Qd = 100 - 2P, Qs = 20 + 3P
    # Returns P, Q
    pass

def elasticity(Qd_func, P, Q):
    # Compute Ed = (dQ/dP) * (P/Q)
    # Example: Qd = 100 - 2P → dQ/dP = -2
    pass