Question

Suppose that the table presented below shows an economy’s relationship between real output and the inputs needed to produce that output:

Input Quantity	Real GDP
150.0	\(400
112.5	300
75.0	200

1. What is productivity in this economy?

2. What is the per-unit cost of production if the price of each input unit is \)2?

3. Assume that the input price increases from \(2 to \)3 with no accompanying change in productivity. What is the new per-unit cost of production? In what direction would the $1 increase in input price push the economy’s aggregate supply curve? What effect would this shift of aggregate supply have on the price level and the level of real output?

4. Suppose that the increase in input price does not occur but, instead, that productivity increases by 100 percent. What would be the new per-unit cost of production? What effect would this change in per-unit production cost have on the economy’s aggregate supply curve? What effect would this shift of aggregate supply have on the price level and the level of real output?

Short answer

1. The productivity of the economy is 2.6667.

2. The per-unit production cost is $0.75.

3. The per-unit production cost is $1.125. The AS curve will move toward the left. The output will decline, and the price will increase.

4. The per-unit production cost is $0.375. The AS curve will move toward the right, increasing the output and reducing the price level.

Step-by-step solution

Productivity of the economy

Productivity is the ratio of total output to total inputs. It measures the efficiency of the economy.

$Productivity=\frac{totaloutput}{totalinputs}=\frac{900}{337.5}=2.6667$

Thus, the productivity of the economy is 2.6667.

Per-unit production cost 

The following formula helps to calculate the per-unit production cost:

$$\begin{gathered} \mathrm{Per}\mathrm{Unit}\mathrm{production}\mathrm{cost}=\mathrm{Input}\mathrm{price}\times \frac{\mathrm{Total}\mathrm{Input}}{\mathrm{Total}\mathrm{Output}} \\ =\$2\times \frac{337.5}{900} \\ =\$0.75 \end{gathered}$$

Thus, at the price of $2 per input, the per-unit production cost is $0.75.

Change in per-unit production cost, AS curve, output, and price level due to a change in the input price

When the input price increases to $3, the per-unit production cost will be as follows:

$$\begin{gathered} \mathrm{Per}\mathrm{Unit}\mathrm{production}\mathrm{cost}=\mathrm{Input}\mathrm{price}\times \frac{\mathrm{Total}\mathrm{Input}}{\mathrm{Total}\mathrm{Output}} \\ =\$3\times \frac{337.5}{900} \\ =\$1.125 \end{gathered}$$

Hence, per-unit production cost has increased to $1.125.

The increase in production cost will reduce the aggregate supply and push the AS curve to the left. So, the real output will decrease with an increase in output price.

Change in per-unit production cost, AS curve, output, and price level due to a change in the productivity

A 100% increase in productivity means that the productivity has become twice because the total output has increased from the same amount of total input.

$$\begin{gathered} Productivity=\frac{TotalOutput}{TotalInput} \\ 2.6667=\frac{900}{337.5} \end{gathered}$$

Double the productivity.

$$\begin{gathered} 2\times 2.6667=\frac{Newtotaloutput}{337.5} \\ Newtotaloutput=1800 \end{gathered}$$

Since the input price is constant at $2, the new per-unit production cost will be as follows:$$\begin{gathered} PerUnitproduction\cos t=Input\cos t\times \frac{Totalinput}{Totaloutput} \\ =\$2\times \frac{337.5}{1800} \\ =0.375 \end{gathered}$$

Since the per-unit production cost has declined due to increased productivity, the aggregate supply will increase. Thus, the AS curve will move to the right. The output will increase with a decline in the price level.