Question

Question 15 Multi part

A) The following represents demand for widgets (a fictional product):

QD=1058−250P−0.0001M−0.5PR

where P is the price of widgets, M is income, and PR is the price of a related (fictional) good, the wodget. Supply of widgets is determined by

QS=2+250P

Widgets are _________, and widgets and wodgets are _____________.

Select one:

a. a normal good; substitutes.

b. an inferior good; substitutes.

c. an inferior good; complements.

d. a normal good; complements.

B) Assume that M=$50,000 and PR=$2.00. The equilibrium price of widgets is ______Answer:

C) The equilibrium quantity of widgets is Answer _____units.

D) Now assume two events occur: income rises to $60,000 and supply conditions change such that QS=6+300P. Solve algebraically for the new equilibrium price of widgets after these two changes.

Answer:_____

E) Solve algebraically for the new equilibrium quantity of widgets after these two changes.

Answer_______

Answer 1

A) c. an inferior good; complements.
(dQD/dM = -0.0001 < 0. So, widgets are inferior. And, dQD/dPR = -0.5 < 0. So, widgets are wodgets are complements.

B) QD=1058−250P−0.0001M−0.5PR = 1058−250P−0.0001(50,000)−0.5(2) = 1058 - 250P - 5 - 1 = 1052 - 250P
At equilibrium, QS = QD. So, we get,
2+250P = 1052 - 250P
So, 250P + 250P = 1052 - 2
So, 500P = 1050
So, P = 1050/500 = 2.1

The equilibrium price of widgets is 2.1

C) Q = 2 + 250P = 2 + 250(2.1) = 2 + 525 = 527
The equilibrium quantity of widgets is 527 units.

D) QD=1058−250P−0.0001M−0.5PR = 1058−250P−0.0001(60,000)−0.5(2) = 1058 - 250P - 6 - 1 = 1051 - 250P
At equilibrium, New QS = New QD. So, we get,
6+300P = 1051 - 250P
So, 300P + 250P = 1051 - 6
So, 550P = 1045
So, P = 1045/550 = 1.9

The equilibrium price of widgets is 1.9

C) Q = 6 + 300P = 6 + 300(1.9) = 6 + 570 = 576
The equilibrium quantity of widgets is 576 units.