Problem:

Suppose the relationship between an economy's aggregate inputs and its 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 real output to total inputs. In this example, productivity is 400/100 = 4.
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 1.1 x 4 = 4.4, 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. Each input would now cost 1.1 x $5 = $5.50. 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. In this example, the per-unit production cost following a 10% increase in both productivity and input prices would be ($5.50 x 100)/$440 = $1.25, the same as before.