Question

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

Q_D = 125,568 – 220P - 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 = 200P – 10,800

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 = $275. 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 145,568 and supply conditions change such that

Q_S = 290P – 27,700. Solve algebraically for the new equilibrium price and quantity of widgets after these two changes.

Answer 1

a. To check whether a good is a normal good or inferior good, we how its demand will change when we change income level. So by looking at its demand function, we can see that m (income) has a negative sign which means if we increase income its demand will decrease, therefore, it is an inferior good. Because inferior goods are those goods whose demand will fall when income increases.

To check if widgets and wodgets are substitutes or complementary good we check how its demand will change when the price of wogdets will increase. We can see that Pr has a positive sign in front of it which means when we increase the price of wodgets demand for widgets will increase which means they are substitute goods. Because substitute goods are those goods that have positive relation between its own demand and the price of its substitute.

b. At M = 55000 and Pr = 275, our Qd will be,

QD = 125,568 – 220P - 0.0001M + 0.5PR

Qd = 125568 - 220P - 0.0001 * 55000 + 0.5 * 275

Qd = 125568 - 220P - 5.5 + 137.5

Qd = 125700 - 220P

Qs = 200P - 10800

For equilibrium,

Qd = Qs

125700 - 220P = 200P - 10800

420P = 136500

P* = 325

Q* = 125700 - 220 * 325 = 54200

C.

d. New Demand, Qd = 145568 - 220P

Qs = 290P - 27700

For equilibrium ,

Qs = Qd

290P - 27700 = 145568 - 220P

410P = 173268

P* = 422.60

Q* = 290 * 422.60 - 27700 = 94855.41