Question

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

Q_D = 14,735 – 200P + 0.0001M - 0.5P_R

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

Q_S = 250P - 800

1. Determine whether widgets are a normal or inferior good, and whether widgets and wodgets are substitutes or complements.
2. Assume that M = $55,000 and P_R = $31.00. Solve algebraically to determine the equilibrium price and quantity of widgets.
3. Generate a supply/demand graph in Excel. Be sure that P is the vertical axis and Q the horizontal. Does the graphical equilibrium correspond to your algebraic equilibrium?
4. Now assume two events occur: demand changes such that the intercept in the demand equation rises to 16,000 and supply conditions change such that

Q_S = 275P + 790. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.

Answer 1

(a)

Q_D = 14,735 – 200P + 0.0001M - 0.5P_R

Coefficient of variable M is positive which means income and quantity demand for widgets is positive. Hence, widgets is normal good.

Coefficient of varibale P_R is negative which means price of related good wodget and demand for widgets is negative. Hence, widgets and wodgets are complementary goods.

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(b)

Q_D = 14,735 – 200P + 0.0001M - 0.5P_R

Put M = 55,000 and P_R= 31

=> Q_D = 14,735 – 200P + 0.0001(55000) - 0.5(31)

=> Q_D = 14,735 – 200P + 5.5- 15.5

=> Q_D = 14,725 – 200P

And Qs = 250P - 800

At equilibrium, Q_D = Qs = Q

=> 14725 - 200P = 250P - 800

=> 14725 + 800 = 250P + 200P

=> 15525 = 450P

=> P = (15525 / 450)

=> P= 34.5

and, Q = 250P - 800

=> Q = 250(34.5) - 800

=> Q = 7825

Equilibrium price is 34.5 and equilibrium quantity is 7825

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(C)

Equilibrium occurs at the intersection of demand and supply curve. At intersection point, equilibrium quantity is 7825 and price is 34.5.

Yes graphical equilibrium corresponds to the algebric equilibrium.

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(d) Now intercept of demand equation rises from 14725 to 16000

New demand equation: QD = 16000 - 200P

New Supply equation: QS = 275P + 790

At new equilibrium point, new demand = new supply

=> 16000 - 200P = 275P + 790

=> 16000 - 790 = 275P + 200P

=> 15210 = 475P

=> P = (15210 / 475)

=> P = 32.02

and Q = 275P + 790

=> Q = 275 (32.02) + 790

=> Q = 9595.5

New equilibrium price is 32.02 and equilibrium quantity is 9595.5