The following represents demand for widgets: QD = 680 – 9P +0.006M – 4PR, where
ID: 1193955 • Letter: T
Question
The following represents demand for widgets: QD = 680 – 9P +0.006M – 4PR, where P is the price of widgets, M is income, and PR is the price of a related good, the wodget. Supply of widgets is determined by QS = 30 + 3P.
A. Assume that in 2010 M = $15,000 and PR = $20. The 2010 equilibrium price of widgets is
B. The 2010 equilibrium quantity of widgets is
C. Now assume two events occur in 2012: income drops to $13,000 and supply conditions change such that QS = 50 + 3P. Solve algebraically for the new equilibrium price of widgets after these two changes.
D. Solve algebraically for the new (2012) equilibrium quantity of widgets after these two changes.
Explanation / Answer
a)
QD = 680 – 9P +0.006M – 4PR = 680 -9P + 0.006*(15000)- 4(20)= 690- 9P
QS = 30 + 3P
FOR EQUILIBRIUM
QD =QS
690- 9P= 30 + 3P
660 =12P
P= 55 IS EQUILIBRIUM PRICE IN 2010
B)
QS = 30 + 3P = 30+ 3(55) =195 IS EQUILIBRIUM QUANTITY IN 2010
C) INCOME DROPS TO 13000, SO NEW DEMAND CURVE WILL BE
QD = 680 – 9P +0.006M – 4PR = 680 -9P + 0.006*(13000)- 4(20)= 678 -9P
QS = 50 + 3P
QD =QS
678 -9P= 50 + 3P
628 = 12P
P= 52.3333 IS EQUILIBRIUM PRICE IN 2012
D)
QS = 50 + 3P = 50+ 3(52.3333) = 207 IS EQUILIBRIUM QUANTITY IN 2012