(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 15to18, 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.