Let's solve the problem **step by step** as requested: --- ## Step 1: **Complete the Cost and Revenue Table** We need to fill in the missing columns: ATC (Average Total Cost), MC (Marginal Cost), MR (Marginal Revenue), and AR/P (Average Revenue/Price). ### **Given Table:** | Q | TC | ATC | MC | TR | MR | AR/P | |---|-----|-----|-----|-----|-----|------| | | 400 | | | | | | | 1 | 600 | | | 400 | | | | 2 | 700 | | | 700 | | | | 3 | 750 | | | 900 | | | | 4 | 850 | | |100 | | | | 5 |100 | | |108 | | | ### **Calculations:** #### **ATC (Average Total Cost):** \[ \text{ATC} = \frac{TC}{Q} \quad (\text{if } Q > ) \] #### **MC (Marginal Cost):** \[ \text{MC} = TC_n - TC_{n-1} \] #### **MR (Marginal Revenue):** \[ \text{MR} = TR_n - TR_{n-1} \] #### **AR/P (Average Revenue/Price):** \[ \text{AR/P} = \frac{TR}{Q} \quad (\text{if } Q > ) \] --- #### **Now Fill the Table:** | Q | TC | ATC | MC | TR | MR | AR/P | |---|-----|---------|------|-----|------|--------| | | 400 | - | - | | - | - | | 1 | 600 | 600 | 200 | 400 | 400 | 400 | | 2 | 700 | 350 | 100 | 700 | 300 | 350 | | 3 | 750 | 250 | 50 | 900 | 200 | 300 | | 4 | 850 | 212.5 | 100 |100 | 100 | 250 | | 5 |100 | 200 | 150 |108 | 80 | 216 | **Explanation:** - ATC is calculated by dividing TC by Q (for Q ≠ ). - MC is the change in TC as Q increases by 1. - MR is the change in TR as Q increases by 1. - AR/P is TR divided by Q (for Q ≠ ). --- ## Step 2: **Determine the Price and Output Selection for the Monopoly** A monopoly maximizes profit where **MR = MC** (as long as P > ATC). ### From the completed table: - At Q = 4: MC = 100, MR = 100 (**MR = MC**) - At Q = 5: MC = 150, MR = 80 (**MC > MR**) So, the **profit-maximizing output is Q = 4**. - The corresponding **price (AR/P)** at Q = 4 is **250**. **Explanation:** The profit-maximizing level is where MR = MC. At Q = 4, both are 100. --- ## **Final Answers** ### i. **Completed Table** (see above). ### ii. **Profit-maximizing output and price:** - **Output (Q):** 4 units - **Price:** $250 ### iii. **Why is Marginal Revenue decreasing?** **Explanation:** For a monopoly, to sell more units, it must lower the price on all units sold, not just the last unit. This causes MR to fall faster than price (AR), and MR is always less than AR after the first unit. Hence, MR decreases as output increases. --- **Summary Table (Final):** | Q | TC | ATC | MC | TR | MR | AR/P | |---|-----|--------|-----|-----|-----|------| | | 400 | - | - | | - | - | | 1 | 600 | 600 | 200 | 400 | 400 | 400 | | 2 | 700 | 350 | 100 | 700 | 300 | 350 | | 3 | 750 | 250 | 50 | 900 | 200 | 300 | | 4 | 850 | 212.5 | 100 |100 | 100 | 250 | | 5 |100 | 200 | 150 |108 | 80 | 216 |