Various beverages are sold by roving vendors at Busch Stadiu

Various beverages are sold by roving vendors at Busch Stadium, home of the Saint Louis Cardinals. Demand and supply of the product are both highly sensitive to changes in the weather. During summer months the demand for ice cold beverages grows rapidly. On the other hand, hot, dry weather has an adverse effect on supply in that it taxes the stamina of the vendor carrying his or her goods up and down many flights of stairs. The only competition to this service maybe beverages purchased at kiosks in the stadium. Demand and supply functions for ice cold beverages per game are as follows QDX = 20,000 – 10,000P + 20,000PK + 2Y + 500T QSX = 2,000 + 60,000P – 900PL – 1,000PC – 200T Where P is the average price of an ice cold beverage ($ per beverage) PK is the average price of beverages sold at kiosks Y is the average income level of baseball fans T is the average daily temperature (F o Degrees) PL is the average price of labor ($ per hour) PC is the average cost of capital in percent 1. When quantity is expressed as a function of price what are the ice cold beverage demand and supply curves when P = $11; PK = $1.50; Y = $25,000; T = 80o F; PL = $10, and PC = 12 % (Note for PC do not use decimal equivalent) 2. Show the supply curve equation with P = f (QSX) 3. Show the demand curve equation with P = f (QDX) 4. Calculate the equilibrium price and quantity 5. Calculate the prices necessary to sell and purchase the following QX: 55,000 to 130,000 beverages in increments of 15,000 beverages 6. Is PK a substitute good or complimentary good? Why?

Solution

QDX = 20,000 – 10,000P + 20,000PK + 2Y + 500T

Putting values, P = $11; PK = $1.50; Y = $25,000; T = 80o F; PL = $10, and PC = 12 %

Qdx = 20000-10000P+20000(1.50) + 2(25000) +500 (800)]

20000-10000P+30000+50000+40000

140000-10000P

QSX = 2,000 + 60,000P – 900PL – 1,000PC – 200T

Qs = 2000+60000P-90(10)-1000(0.12)-200(800)

Qs = 2000+60000P-900-1200-160000

Qs = 60000P-160100

2. Show the supply curve equation with P = f (QSX)

60000P = Qs+160100

P = Qs/60000+160100/60000

3. Show the demand curve equation with P = f (QDX)

Qd = 140000-10000P

P = Qd/10000+14

4. Equilibrium price is determined where demand is equal to supply

Put demand equaltion equal to supply equation to ind equilibrium price and equilibrium quantity

5. By putting values of 55000, 70000, 95000, 11000, 125000, 140000 in qdx and Qfx functions to find the prices.

6. Pk is a substitute good because it is showning positive relation with the demand of given good.

4. Calculate the equilibrium price and quantity 5. Calculate the prices necessary to sell and purchase the following QX: 55,000 to 130,000 beverages in increments of 15,000 beverages 6. Is PK a substitute good or complimentary good? Why?