2. Every fall, once the weather begins to cool off, demand for pumpkin spice lattes (PSLs) picks up. This past fall, demand for PSLs in Nacogdoches was estimated to be Q D = 10−0.5P where P is the price of a PSL in dollars, and Q D is the quantity demanded in thousands per day. The supply is given by Q S = −5+2P.
(a) What are the equilibrium price and quantity of PSLs in Nacogdoches?
(b) What is the price elasticity of demand at the equilibrium point you found in part (a)?
(c) Could Starbucks (or other coffee shops) increase revenue by changing their price? Explain in a sentence or two.
(d) Suppose Java Jacks, a local coffee shop, wants to capitalize on the popularity of these drinks and releases a local-inspired blueberry-infused pumpkin flavored latte as an alternative to a traditional PSL. What would be the effect on the elasticity of demand for regular PSLs?
(a) At equilibrium, demand = supply. So, QD = QS
So, 10−0.5P = −5+2P
So, 2P + 0.5P = 10 + 5
So, 2.5P = 15
So, P = 15/2.5
So, P = 6
Q = −5+2P = -5 + 2*(6) = -5 + 12 = 7
So, Q = 7
(b) Q D = 10−0.5P
dQ/dP = -0.5
Elasticity, E = (dQ/dP)*(P/Q) = (-0.5)*(6/7)
So, E = -0.43
(c) Absolute value of elasticity is less than 1 so demand is inelastic. Thus, revenue can be increased by increasing the price.
(d) Demand for regular PSLs will become more elastic because of increase in the number of substitutes.
2. Every fall, once the weather begins to cool off, demand for pumpkin spice lattes (PSLs)...