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    Market equilibrium price and output combination

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    1. The following relations describe monthly demand and supply relations for dry cleaning services in the metropolitan area:

    QD = 500,000 - 50,000P (Demand)

    QS = -100,000 + 100,000P (Supply)

    where Q is quantity measured by the number of items dry cleaned per month and P is average price in dollars.

    A. At what average price level would demand equal zero?

    B. At what average price level would supply equal zero?

    C. Calculate the equilibrium price/output combination.

    2. The Creative Publishing Company (CPC) is a coupon book publisher with markets in several southeastern states. CPC coupon books are sold directly to the public, sold through religious and other charitable organizations, or given away as promotional items. Operating experience during the past year suggests the following demand function for CPC's coupon books:

    Q = 5,000 - 4,000P + 0.02Pop + 0.25I + 1.5A,

    where Q is quantity, P is price ($), Pop is population, I is disposable income per household ($), and A is advertising expenditures ($).

    A.Determine the demand faced by CPC in a typical market in which P = $10, Pop = 1,000,000 persons, I = $60,000, and A = $10,000.

    B.Calculate the level of demand if CPC increases annual advertising expenditures from $10,000 to $15,000.

    C.Calculate the demand curves faced by CPC in parts A and B.

    3. The Eastern Shuttle, Inc., is a regional airline providing shuttle service between New York and Washington, D.C. An analysis of the monthly demand for service has revealed the following demand relation:

    Q = 26,000 - 500P - 250POG + 200IB - 5,000S,

    where Q is quantity measured by the number of passengers per month, P is price ($), POG is a regional price index for other consumer goods (1967 = 1.00), IB is an index of business activity, and S, a binary or dummy variable, equals 1 in summer months and 0 otherwise.

    A.Determine the demand curve facing the airline during the winter month of January if POG = 4 and IB = 250.

    B.Determine the demand curve facing the airline, quantity demanded, and total revenues during the summer month of July if P = $100 and all other price-related and business activity variables are as specified previously.

    4. Eye-de-ho Potatoes is a product of the Coeur d'Alene Growers' Association. Producers in the area are able to switch back and forth between potato and wheat production depending on market conditions. Similarly, consumers tend to regard potatoes and wheat (bread and bakery products) as substitutes. As a result, the demand and supply of Eye-de-ho Potatoes are highly sensitive to changes in both potato and wheat prices.

    Demand and supply functions for Eye-de-ho Potatoes are as follows:

    QD = -1,450 - 25P + 12.5PW + 0.1Y, (Demand)

    QS = -100 + 75P - 25PW - 12.5PL + 10R, (Supply)

    where P is the average wholesale price of Eye-de-ho Potatoes ($ per bushel), PW is the average wholesale price of wheat ($ per bushel), Y is income (GDP in $ billions), PL is the average price of unskilled labor ($ per hour), and R is the average annual rainfall (in inches). Both QD and QS are in millions of bushels of potatoes.

    A. When quantity is expressed as a function of price, what are the Eye de ho Potatoes demand and supply curves if PW = $4, Y = $15,000 billion, PL = $8, and R = 20 inches?

    B. Calculate the surplus or shortage of Eye-de-ho Potatoes when P = $1.50, $2, and $2.50.

    C. Calculate the market equilibrium price/output combination.

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    Solution Preview

    a. Demand is zero when quantity demanded falls to zero. Given the demand function we need to solve:
    0 = 500000 - 50000P
    or P = 10.

    So quantity demanded falls to zero when price goes to 10.

    b. Similarly, quantity supplied falls to zero when
    0 = -100000 + 100000P
    or P = 1.

    Hence quantity supplied falls to zero when price goes to 1.

    c. To find the equilibrium we need to solve:
    QD = QS
    or 500000 - 50000P = -100000 + 100000P
    or 600000 = 150000P
    or P = 4.

    Plug in either the demand or supply function and we get:
    QD = 500000 - 50000*4 = 300000.

    Hence, equilibrium price is 4, and equilibrium quantity is 300000.

    2. Demand function for the company is given as

    Solution Summary

    Calculate the market equilibrium price/output combination.