Analysis of demand and supply curves

1. Demand Curve Analysis.

Papa's Pizza, Ltd., provides delivery and carryout service to the city of South Bend, Indiana. An analysis of the daily demand for pizzas has revealed the following demand relation:

Q = 1,400 - 100P - 2PS + 0.01CSP + 750S

where Q is the quantity measured by the number of pizzas per day, P is the price ($), PS is a price index for soda pop (1992 = 100), CSP is the college student population and S, a binary or dummy variable, equals 1 on Friday, Saturday and Sunday, zero otherwise.

A. Determine the demand curve facing Papa's Pizza on Tuesdays if P = $10, PS = 125, and CSP = 35,000, and S = 0.

B. Calculate the quantity demanded and total revenues on Fridays if all price-related variables are as specified above.

2. Supply Curve Analysis.

Credible Switches, Inc., is a distributor of generic safety switches used in the washing machines and dryers. Based on an analysis of monthly cost and output data, the company has estimated the following relation between the marginal cost MC (wholesale cost plus distribution cost per unit) and monthly output:

MC = dTC/dQ = $2 + $0.00001Q

A. Calculate marginal cost at 400,000, 500,000, and 600,000 units of output.

B. Express output as a function of marginal cost. Calculate the level of output at which MC = $5, $8, and $10.

C. Calculate the profit-maximizing level of output if prices are stable in the industry at $8 per switch and, therefore, P = MR = $8.

D. Again assuming prices are stable in the industry, derive CSI's supply curve for switches. Express price as a function of quantity and quantity as a function of price.

3. Market Equilibrium.

Various beverages are sold by roving vendors at Busch Stadium, home of the St. Louis Cardinals. Demand and supply of the product are both highly sensitive to changes in the weather. During hot summer months, 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 for this service is provided by the beverages that can be purchased at kiosks located throughout the stadium.

Demand and supply functions for ice-cold beverages per game are as follows:
QD = 20,000 - 20,000P + 7,500PK + 0.8Y + 500T (Demand)
QS = 1,000 + 12,000P - 900PL - 1,000PC - 200T (Supply)

where P is the average price of ice-cold beverage ($ per beverage), PK is the average price of beverages sold at the kiosks ($ per beverage), Y is disposable income per household for baseball fans, T is the average daily high temperature (degrees), PL is the average price of unskilled labor ($ per hour), and PC is the average cost of capital (in percent).

A. When quantity is expressed as a function of price, what are the ice-cold beverage demand and supply curves if P = $5, PK = $4, Y = $62,500, T = 80 degrees, PL = $10, and PC = 12%.

B. Calculate the surplus or shortage of ice-cold beverage when P = $4, $5, and $6.

C. Calculate the market equilibrium price-output combination.