To solve this problem using Keynesian-cross analysis, we need to determine the level of government spending $G$ that will bring the equilibrium level of income $Y$ to 1,000. Let's go step by step:

Step 1: Consumption Function

The consumption function is given as:

$C = 100 + 0.6(Y - T)$

Where:

• $C$ is consumption,
• $Y$ is income,
• $T$ is taxes, and
• $100$ is the autonomous consumption.

Since $T = 100$, we can substitute this into the consumption function:

$C = 100 + 0.6(Y - 100)$ $C = 100 + 0.6Y - 60$ $C = 40 + 0.6Y$

Step 2: Aggregate Expenditure

The aggregate expenditure (AE) in a simple Keynesian model is:

$AE = C + I + G$

Where:

• $C$ is consumption (which we just calculated),
• $I$ is planned investment, and
• $G$ is government spending.

Given that planned investment $I = 100$, the aggregate expenditure becomes:

$AE = (40 + 0.6Y) + 100 + G$ $AE = 140 + 0.6Y + G$

Step 3: Equilibrium Condition

In equilibrium, aggregate expenditure $AE$ equals income $Y$. So:

$Y = 140 + 0.6Y + G$

Step 4: Solve for $G$

We want the equilibrium income $Y$ to be 1,000. So we substitute $Y = 1,000$ into the equation:

$1000 = 140 + 0.6(1000) + G$ $1000 = 140 + 600 + G$ $1000 = 740 + G$ $G = 1000 - 740$ $G = 260$

Conclusion:

The level of government spending $G$ needed to make equilibrium income $Y$ equal to 1,000 is 260.

Thus, the correct answer is:

$\boxed{b. \ 260}$

Would you like a more detailed breakdown or have any questions?

Related Questions:

1. How does the marginal propensity to consume (MPC) affect the multiplier in Keynesian economics?
2. What is the formula for calculating the government spending multiplier in a closed economy?
3. How would the solution change if planned investment $I$ were 150 instead of 100?
4. What happens to the equilibrium income if taxes $T$ increase by 50 units?
5. Can you explain how fiscal policy (like changing $G$) affects aggregate demand in this model?

Tip:

In the Keynesian-cross model, increasing government spending is an effective tool for stimulating the economy and achieving higher levels of output. The size of the effect depends on the marginal propensity to consume (MPC).