Question

1a) Suppose your company is faced with the following demand curve: Q^D = 600 – 100 P. The price elasticity of demand, E^D , at a price of $5 equals _____, and the price elasticity of demand, E^D, at a price of $1 equals _____

1b) Assume that the demand equation for exercise watches, such as the Fitbit, is Q^D = 2,200 – 15 P and the supply equation is Q^S = 15 P – 800. After a favorable study shows that using exercise watches significantly reduces users' weights, quantity demanded increases by 300 at every price. The new equilibrium price will be _____ and the new equilibrium quantity will be ____

1c)In the market for oranges, we observe that the equilibrium price increased and the equilibrium quantity increased. What could have caused this change?

1d)The demand curve for a good is Q = 80 – 0.20 P, where Q is the quantity demanded and P is the price per unit. This good's inverse demand curve is:

Answer 1

Solution:

a) Demand curve: Qd = 600 - 100*P

At P = $5, Qd = 600 - 100*5 = 100 units

At P = $1, Qd = 600 - 100*1 = 500 units

Price elasticity of demand, ed =

From the demand equation, we know that = -100, so

Elasticity at price of $5 = (-100)*(5/100) = -5

Elasticity at price of $1 = (-100)*(1/500) = - 0.2

b) Since, quantity demanded increases by 300 at every price, it simply means a rightward shift in demand curve. So, for new demand function, the intercept increases by 300. New demand function is:

Qd' = Qd + 300

Qd' = 2200 - 15*P + 300 = 2500 - 15*P

Supply curve remains unchanged: Qs = 15*P - 800

New equilibrium: Qd' = Qs

2500 - 15*P = 15*P - 800

(15 + 15)*P = 2500 + 800

30*P = 3300

P = 3300/30 = $110

Equilibrium quantity, Q = 2500 - 15*110 = 850 watches

c) In the orange market, both, equilibrium quantity and equilibrium price increased. So, the change must have been such that both, quantity and price move together. When a supply curve shifts, the price and quantity change in opposite direction. So, it must be a shift in demand curve. The shift must be outward, such that demand increase results in higher equilibrium price and also the higher quantity.

Another reason could be that both supply and demand curve shift, but demand curve must shift outward or rightward and this shift must be higher than the shift in supply curve (in any direction).

d) Good's demand curve: Q = 80 - 0.20*P

Inverse demand curve is simply price expressed in terms of quantity:

Q = 80 - 0.20*P

0.20*P = 80 - Q

P = (80 - Q)/0.20

P = 400 - 5*Q

This is the required inverse demand function.