Assume that, without taxes, the consumption schedule of an economy is as follows.

GDP, Billions	Consumption, Billions
\(100	\)120
200	200
300	280
400	360
500	440
600	520
700	600

1. Graph this consumption schedule and determine the MPC.

2. Assume now that a lumpsum tax is imposed such that the government collects $10 billion in taxes at all levels of GDP. Graph the resulting consumption schedule and compare the MPC and the multiplier with those of the pretax consumption schedule.

The consumption schedule depends on the level of income or GDP. Therefore, the independent factor, GDP, will be on the X-axis and consumption schedule.

Since income and consumption are increasing at a constant rate, the consumption schedule will be a positively sloped straight line.

As consumption constantly increases by $80 billion for every increase of $100 billion in GDP, the MPC for this consumption schedule is as follows:

$$\begin{gathered} MPC=\frac{∆Consumption}{∆Income} \\ MPC=\frac{80}{100} \\ MPC=0.8 \end{gathered}$$

Therefore, the MPC is 0.8.

A change of $80 billion in total spending increases the income by $100 billion.

$$\begin{gathered} k=\frac{1}{1-MPC} \\ k=\frac{1}{1-0.8} \\ k=5 \end{gathered}$$

Hence, the multiplier is 5.

Since a lumpsum tax of $10 billion is imposed at each level of GDP, the disposable income declines by $10 billion each time.

As the disposable income has declined, the consumption will also reduce by the taxes in accordance with the MPC. Since we have MPCequals to 0.8, the consumption will decrease as follows:

$$\begin{gathered} MPC=∆Tax\times ∆Consumption \\ MPC=\$10billion\times 0.8 \\ MPC=\$8billion \end{gathered}$$

Therefore, the consumption after tax will decline by $8 billion. The income after tax and respective consumption schedule after tax is as follows:

The respective graph is as follows:

The consumption schedule shifts toward the left due to a decline in disposable income and consumption.

Since the income has declined constantly by $100 billion, and consumption declined constantly by $80 billion, the difference between two consecutive income levels and consumption is still the same. Thus, change in consumption and change in income is the same as in pretax conditions. Therefore, MPC is constant at 0.8.

Since MPC and MPS are constant, therefore multiplier is also constant at 5.