In a closed economy with no government, the value of the multiplier is 3. By how much will consumption increase if investment increases by $300?

The multiplier ($k$) is given as 3, and the increase in investment ($\Delta I$) is $300. The formula for the change in income is:

$$\Delta Y = k \times \Delta I$$

$\Delta Y = 3 \times \$300$ $\Delta Y = \$900$

In a closed economy with no government, the multiplier formula is $k = \frac{1}{1 - MPC}$.
Given $k = 3$:

$$3 = \frac{1}{1 - MPC}$$ $$3(1 - MPC) = 1$$ $$3 - 3MPC = 1$$ $$3MPC = 2$$ $$MPC = \frac{2}{3}$$

The increase in consumption is given by:

$$\Delta C = MPC \times \Delta Y$$

$\Delta C = \frac{2}{3} \times \$900$ $\Delta C = 2 \times \$300$ $\Delta C = \$600$

The increase in consumption is $600.

The final answer is $\text{C}$