Question 6.1

1. Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity. The quantity of output, measured in terms of pounds of ice, is given in the accompanying table.

Quantity of
electricity (kilowatts)		 Quantity of ice
(pounds)
0 0
1 1,000
2 1,800
3 2,400
4 2,800

  1. What is the fixed input? What is the variable input?

    The fixed input is the 10-ton machine, and the variable input is electricity.

  2. Construct a table showing the marginal product of the variable input. Does it show diminishing returns?

    As you can see from the declining numbers in the third column of the accompanying table, electricity does indeed exhibit diminishing returns: the marginal product of each additional kilowatt of electricity is less than that of the previous kilowatt.

    Quantity
    of electricity
    (kilowatts)    		 Quantity of
    ice (pounds)    		 Marginal product
    of electricity
    (pounds per
    kilowatt)
    0 0
    1,000
    1 1,000
    800
    2 1,800
    600
    3 2,400
    400
    4 2,800

  3. Suppose a 50% increase in the size of the fixed input increases output by 100% for any given amount of the variable input. What is the fixed input now? Construct a table showing the quantity of output and marginal product in this case.

    A 50% increase in the size of the fixed input means that Bernie now has a 15-ton machine. So the fixed input is now the 15-ton machine. Since it generates a 100% increase in output for any given amount of electricity, the quantity of output and marginal product are now as shown in the accompanying table.

    Quantity of
    electricity
    (kilowatts)    		 Quantity of ice
    (pounds)    		 Marginal product
    of electricity
    (pounds per
    kilowatt)
    0 0
    2,000
    1 2,000
    1,600
    2 3,600
    1,200
    3 4,800
    800
    4 5,600