(a) Calculate Current Quantity Demanded:
- Start with the demand equation:
Qd=800−20P+0.5Y
- Substitute the current values (P = 15,Y=600):
Qd=800−20(15)+0.5(600)
- Calculate the components:
- Price component: 20∗15=300
- Income component: 0.5∗600=300
- Solve for Qd:
Qd=800−300+300
Qd=800 units.
The current quantity demanded is 800 units.
(b) Calculate New Quantity Demanded (Ceteris Paribus):
- Apply the ceteris paribus assumption: This means only the price (P) changes. Income (Y) is held constant at $600.
- Use the new price (P = $18) in the equation:
Qd′=800−20(18)+0.5(600)
- Calculate the new components:
- New price component: 20∗18=360
- Income component (unchanged): 0.5∗600=300
- Solve for the new Qd (Qd'):
Qd′=800−360+300
Qd′=740 units.
The new quantity demanded is 740 units.
5. Calculate the change in quantity demanded:
Change=NewQd−OldQd=740−800=−60 units.
Conclusion: With the price increase from $15 to $18, and holding income constant (ceteris paribus), the quantity demanded decreases by 60 units. This calculation demonstrates how economists use models and assumptions to isolate the effect of a single variable.