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Analysis of demand and supply curves

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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.

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Solution Preview

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.

Q = 1,400 - 100P - 2PS + 0.01CSP + 750S
Put PS=125
CSP=35000
S=0
Q=1400-100P-2*125+0.01*35000+750*0=1500-100P
Q=1500-100P

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

Q = 1,400 - 100P - 2PS + 0.01CSP + 750S
Put PS=125
CSP=35000
S=1
P=$10
Q=1400-100*10-2*125+0.01*35000+750*1=1250
Quantity demanded=1250 units
Total Revenue=P*Q=10*1250=$12500

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 ...

Solution Summary

There are three problems. Solution to first problem depicts the methodology to find out the demand curve in the given case. Solution to second problem explains the steps to calculate values of desired parameters. Solution to third problems calculates the equilibrium price output combination.

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Demand & Supply Curves, Analysis, Comparative Statics & Quantity

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Demand and Supply Curves.
The following relations describe demand and supply conditions in the oil industry, where Q is quantity measured in millions of barrels and P is price in dollars:
QD = 525,000 - 7,500P (Demand)

QS = - 150,000 + 15,000P (Supply)
Complete the following table (COPY AND PASTE THE TABLE TO YOUR WORD DOCUMENT)
Price (1) Quantity Supplied (2) Quantity Demanded (3) Surplus (+) or Shortage ( - ) (4) = (2) - (3)
$35
30
25
20
15
2. Demand Analysis. The demand for high-definition television sets (HDTV) is often described as highly cyclical, and very sensitive to HDTV prices and interest rates. Given these characteristics, describe the effect of each of the following in terms of whether it would increase or decrease the quantity demanded or the demand of HDTVs. Moreover, when price is expressed as a function of quantity, indicate whether the effect of each of the following is an upward or downward movement along a given demand curve or instead involves an outward or inward shift in the relevant demand curve for HDTVs. Explain your answers.
A. A decrease in HDTV prices
B. A fall in interest rates
C. A rise in interest rates
D. A severe economic recession
E. A robust economic expansion
3. Comparative Statics.
Demand and supply conditions in the steel market are important concerns to business and government decision makers. Some of the following factors have the potential to influence the demand or quantity demanded of raw steel. Influences on the supply or quantity supplied may also result. Holding all else equal, describe these influences as increasing or decreasing, and indicate the direction of the resulting movement along or shift in the relevant curve(s).
A. Increases in the U. S. Department of Transportation's mileage requirements for car fleets.
B. Public outcry at the poor condition of the nation's interstate freeway system.
C. New alloys that increase steel's tensile strength are created.
D. A severe recession.
E. A new technology reduces the production cost of raw steel by one-third.
4. Quantity Demanded.
Gurgling Springs, Inc. is a bottler of natural spring water distributed throughout the New England states. Five-gallon containers of GSI spring water are regionally promoted and distributed through grocery chains. Operating experience during the past year suggests the following demand function for its spring water:
Q = 250 - 100P + 0.0001Pop + 0.003I + 0.003A
where Q is quantity in thousands of five-gallon containers, P is price ($), Pop is population, I is disposable income per capita ($), and A is advertising expenditures ($).
A. Determine the demand curve faced by CPI in a typical market where P = $4, Pop = 4,000,000 persons, I = $50,000 and A = $400,000. Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.
B. Calculate the quantity demanded at prices of $5, $4, and $3.
C. Calculate the prices necessary to sell 1,250, 1,500, and 1,750 thousands of five-gallon containers.

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