Equilibrium Analysis
1. Problem 1: Effects on equilibrium price (P) and quantity demanded (QD) due to changes in economic factors.
1. If consumer income increases:
- For a normal good, demand increases, shifting the demand curve right.
- This raises equilibrium price and quantity.
2. If the rent that the firm pays decreases:
- This reduces production costs, shifting supply curve right.
- This lowers the equilibrium price and raises quantity.
3. If the expected price of the good decreases:
- Consumers expect lower future prices, reducing current demand.
- Demand curve shifts left, lowering P and QD.
4. If the price of a substitute good increases:
- Demand for the good increases as consumers switch.
- Demand curve shifts right, raising P and QD.
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2. Problem 2: Given curves:
Demand: $$Q_D = 800 - 2P$$
Supply: $$Q_S = 200 + P$$
1. Find equilibrium price:
Set $$Q_D=Q_S$$
$$800 - 2P = 200 + P$$
Simplify:
$$800 - 200 = 2P + P$$
$$600 = 3P$$
$$P^* = \frac{600}{3} = 200$$
2. Find equilibrium quantity:
Substitute $$P^*$$ into one curve:
$$Q^* = 800 - 2(200) = 800 - 400 = 400$$
3. Equilibrium on curves:
Demand curve: $$y = 800 - 2x$$ (price on x-axis, quantity y?) or as given.
Supply curve: $$y = 200 + x$$
The intersection point is at $$P=200, Q=400$$.
4. For $$P=300$$:
Demand: $$Q_D = 800 - 2(300) = 800 - 600 = 200$$
Supply: $$Q_S = 200 + 300 = 500$$
Since supply > demand, there is excess supply (surplus).
Surplus value: $$500 - 200 = 300$$
5. For $$P=100$$:
Demand: $$Q_D=800 - 2(100)=800 - 200=600$$
Supply: $$Q_S=200 + 100=300$$
Since demand > supply, there is excess demand (shortage).
Shortage value: $$600 - 300 = 300$$
Final answers:
Equilibrium price = 200
Equilibrium quantity = 400
Excess supply at P=300 = 300 units
Excess demand at P=100 = 300 units