Problem:

Suppose an economy's relationship between its aggregate inputs and output can be represented by the following table, in which inputs and real GDP are expressed in billions:

1. What is the productivity level in this economy?
2. Suppose each input costs $5. What is the per unit production cost at each level of output?
3. Suppose productivity increases by 10% with no change in input prices. Calculate the new per unit production cost.
4. Alternatively, suppose input prices increase by 10% with no change in productivity. Calculate the new per unit production cost.
5. True or false: "An equal percentage increase in productivity and input prices will have no impact on per unit production costs."

Answer:

1. Productivity is measured as the ratio of total output to total inputs. In this example, productivity is 4. 4 = $400/100.
2. Production cost is measured as the price of each input times its price. Per unit production cost is this amount divided by total output, or real GDP. In this example, per unit production cost at each level of output is $1.25. $1.25 = ($5 x 100)/$400 = ($5 x 105)/$420 =($5 x 110)/$440 =($5 x 115)/$460.
3. The new productivity level is 4.4 = 1.1 x 4, a 10% increase over its previous level. This means that 100 billion units of inputs could produce 100 x 4.4 = $440 billion of real GDP. The new per unit production cost is ($5 x 100)/$440 = $1.14, a drop of 10%.
4. Inputs would now cost $5.50 = 1.1 x 5. Per unit production cost is ($5.50 x 100)/$400 = $1.375, an increase of 10% over its previous value of $1.25.
5. True. Per unit production cost is the ratio of total input cost to total output. If both numerator and denominator increase in proportion, the ratio is unchanged.