Give step-by-step solution with explanation and final answer:

rewrite the question alsoTotsPoses, Incorporated, a profit-maximizing business, is the only photography business in town that speciali

Question

Give step-by-step solution with explanation and final answer: 

rewrite the question alsoTotsPoses, Incorporated, a profit-maximizing business, is the only photography business in town that specializes in
portraits of small children. George, who owns and runs TotsPoses, expects to encounter an average of eight customers
per day, each with a reservation price shown in the following table. Assume George has no fixed costs, and his cost of
producing each portrait is $25.
1 | se |
a | 38 |
7 1 2 |
a. Suppose George is permitted to charge two prices. He knows that customers with a reservation price above $30
never bother with coupons, whereas those with a reservation price of $30 or less always use them. At what level
should George set the list price of a portrait? At what level should he set the discount price? How many photo
portraits will he sell at each price?
List price of a portrait: $ IV]
Number of portraits to be sold at the list price: [4 & portraits
Discount price of a portrait: $ M
Number of portraits to be sold at the discounted price: £5 portraits
b. In this case, what is George's economic profit and how much consumer surplus is generated each day?
Economi

VIPSolutions · Accepted Answer

**Let's rewrite and solve the question step-by-step:**

---

### **Question (Reworded):**

TotsPoses, Inc. specializes in children's portraits and faces 8 customers per day, each with a different reservation (maximum willing to pay) price, as shown in the table. Each photo costs $25 to produce. George can charge two prices: a list price for customers with a reservation price above $30, and a discount price for those at $30 or less.

**a.** What should the list and discount prices be? How many portraits will be sold at each price?

**b.** What are George's daily economic profit and the consumer surplus under this pricing strategy?

---

### **Step-by-Step Solution:**

#### **Step 1: Review Customer Reservation Prices**

| Customer | Reservation price ($) |
|----------|----------------------|
| 1        | 50                   |
| 2        | 46                   |
| 3        | 42                   |
| 4        | 38                   |
| 5        | 34                   |
| 6        | 30                   |
| 7        | 26                   |
| 8        | 22                   |

#### **Step 2: Set Prices and Quantities**
- **List price:** Customers with reservation price above $30
  - These are customers 1, 2, 3, 4, and 5 (prices: $50, $46, $42, $38, $34)
  - The highest price at which all 5 will buy is $34 (since customer 5's max is $34).

- **Discount price:** Customers with reservation price $30 or less
  - These are customers 6, 7, and 8 (prices: $30, $26, $22)
  - The highest price at which all 3 will buy is $22 (since customer 8's max is $22).

#### **BUT:**  
The question states that people with reservation price $30 or less *always* use the coupon (discount price). Those above $30 *never* do.  
So, set the **discount price at $30**, so customers 6, 7, and 8 can buy if their reservation price is at least $22, but at $30 only customer 6 will buy (since $30 ≥ $30, but $26 and $22 < $30).

So:
- **List price:** $38 (since customer 4's max is $38; customer 5 would use coupon if price is set higher)
- **Discount price:** $30
- **Number at list price:** 4 (customers 1, 2, 3, 4)
- **Number at discount price:** 1 (customer 6)
- **Total portraits sold:** 5

#### **Step 3: Economic Profit**

- **Revenue from list price:** $38 × 4 = $152
- **Revenue from discount price:** $30 × 1 = $30
- **Total revenue:** $152 + $30 = $182
- **Total cost:** $25 × 5 = $125
- **Economic profit:** $182 - $125 = **$57**

#### **Step 4: Consumer Surplus**

- For customers at list price (who pay $38 but would pay more):
  - Customer 1: $50 - $38 = $12
  - Customer 2: $46 - $38 = $8
  - Customer 3: $42 - $38 = $4
  - Customer 4: $38 - $38 = $0
- For customer at discount price:
  - Customer 6: $30 - $30 = $0

**Total consumer surplus:** $12 + $8 + $4 + $0 + $0 = **$24**

---

### **Final Answers:**

#### **a. Pricing and Quantities**
- **List price:** $38
- **Number of portraits at list price:** 4
- **Discount price:** $30
- **Number of portraits at discount price:** 1

#### **b. Economic Profit and Consumer Surplus**
- **Economic profit:** $57
- **Consumer surplus:** $24

---

**Boxed Final Answers:**
- Economic profit: **$57**
- Consumer surplus: **$24**
- Number of portraits at discount price: **1**

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