Questions: Question 7 (10 points) Tarragona had been expecting a 50 million investment spending for a new golf resort, but the contract was canceled. Tarragona's governor estimates that this will cost the region 300 million in total economic activity. What is the governor's estimate of the multiplier and marginal propensity to consume. Multiplier =5 and MPC =0.17 Multiplier =6 and MPC=0.83 Multiplier =5 and MPC =0.83 Multiplier =6 and MPC =0.17

The answer is the third one: Multiplier \(=5\) and MPC \(=0.83\).

Explanation:

1. Understanding the Multiplier Effect: The multiplier effect refers to the proportional amount of increase in final income that results from an injection of spending. It is calculated as: \[ \text{Multiplier} = \frac{\text{Change in Total Economic Activity}}{\text{Initial Change in Spending}} \]

2. Calculating the Multiplier: Given that the initial investment spending was expected to be \$50 million and the total economic activity loss is estimated at \$300 million, the multiplier can be calculated as: \[ \text{Multiplier} = \frac{300}{50} = 6 \]

3. Understanding the Relationship Between Multiplier and MPC: The multiplier is also related to the marginal propensity to consume (MPC) by the formula: \[ \text{Multiplier} = \frac{1}{1 - \text{MPC}} \]

4. Calculating the MPC: If the multiplier is 6, we can set up the equation: \[ 6 = \frac{1}{1 - \text{MPC}} \] Solving for MPC: \[ 1 - \text{MPC} = \frac{1}{6} \] \[ \text{MPC} = 1 - \frac{1}{6} = \frac{5}{6} \approx 0.83 \]

5. Evaluating the Options:

   • Option 1: Multiplier \(=5\) and MPC \(=0.17\) - Incorrect, as the calculated multiplier is 6.
   • Option 2: Multiplier \(=6\) and MPC \(=0.83\) - Correct, matches our calculations.
   • Option 3: Multiplier \(=5\) and MPC \(=0.83\) - Incorrect, as the calculated multiplier is 6.
   • Option 4: Multiplier \(=6\) and MPC \(=0.17\) - Incorrect, as the calculated MPC is 0.83.

In summary, the correct answer is the second option: Multiplier \(=6\) and MPC \(=0.83\).