# A Procedure to Set Prices and Select Inventory in Thinly Traded Markets Using Data from eBay

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

## 3. Results

#### 3.1. Listed Items and Duration

#### 3.2. Determining the Distribution of Listed Items

#### 3.3. Duration and Prices

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

- Let ${\mathrm{n}}_{\mathrm{j}}$ be the number of items kept in the portfolio and let j be the number of iterations (j = 0, 1, 2, …).
- when j = 0, ${\mathrm{n}}_{0}=319$.

- Let C be the total cost of items based on current cycle’s portfolio.
- ${\mathrm{C}}_{\mathrm{j}}=\mathrm{cos}\mathrm{t}/{\mathrm{n}}_{\mathrm{j}}$

- Let α be the cost of an item, T be the duration of the listing, m be the index of items kept in the jth cycle. The cost to source an item is assumed to increase in proportion to duration based on data from the original portfolio,
- ${\mathsf{\alpha}}_{\mathrm{m}}$=${\mathrm{C}}_{\mathrm{j}}{\ast \mathrm{T}}_{\mathrm{m}}$

- Compare each items’ profit ${\mathsf{\pi}}_{\mathrm{m}}$ vs. cost ${\mathsf{\alpha}}_{\mathrm{m}}$ such that if ${\mathsf{\pi}}_{\mathrm{m}}$ >${\mathsf{\alpha}}_{\mathrm{m}}$, keep the item in the portfolio. Otherwise, delete the item from the portfolio.
- Recalculate ${\mathrm{n}}_{\mathrm{j}}$
- Repeat this process until there is no ${\mathsf{\pi}}_{\mathrm{m}}$<${\mathsf{\alpha}}_{\mathrm{m}}$ to obtain the final optimal portfolio.

- proc import out=my_Ebay
- datafile=‘C:\SAS\Ebay’
- dbms=xlsx replace;
- sheet=”Orig data”my_Ebay
- run;
- /*Add column of 1/T=orig d*/
- data my_Ebay;
- set my_Ebay;
- orig_d=1/Dur__Months;
- run;
- sheet="Orig data";
- run;
- proc contents data=my_Ebay;
- run;
- /*Add column of 1/T=orig_d*/
- data my_Ebay;
- set my_Ebay;
- orig_d=1/Dur__Months;
- k=_N_;
- fact_k=fact(k);
- run;
- /*calculate the total orig d*/
- proc sql;
- select sum(orig_d)/count(*) into: final_d
- from my_Ebay;
- quit;
- %put &final_d.;
- /*test count*/
- proc sql;
- select count(*) from my_Ebay;
- quit;
- /*calculate p*/
- data my_Ebay;
- set my_Ebay;
- p=exp(-&final_d.)*(&final_d.*k)/fact_k;
- run;

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**Figure 1.**The Poisson distribution for λ = 68.65 showing the probability of selling at least k items in a month.

**Figure 4.**The relationship between cost and price for the original (Orig) and optimal (Opt) portfolio.

Listed Quantity | 319 | 600 | 900 | 1200 | 1500 | 1800 | 2100 |
---|---|---|---|---|---|---|---|

Lambda (λ) | 68.65 | 129.14 | 193.70 | 258.27 | 322.84 | 387.41 | 451.97 |

Maximum expected gross profit | USD 5798 | USD 11,633 | USD 18,045 | USD 24,559 | USD 31,142 | USD 37,775 | USD 44,444 |

**Table 2.**The distribution of the optimal portfolio of items. Gross profit and cost are the contribution to overall profit and the cost of goods sold. Weighted profit is the percent of gross profit multiplied by average gross profit (USD 140.57).

Median Split Category | Gross Profit | Item Cost | Weighted Profit (per Item) |
---|---|---|---|

High profit, sold fast (HF) | 70.37% | 50.62% | USD 104.85 |

High profit, sold slow (HS) | 1.23% | 1.23% | USD 22.43 |

Low profit, sold fast (LF) | 28.40% | 48.15% | USD 5.93 |

Low profit, sold slow (LS) | 0.00% | 0.00% | USD 0.00 |

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## Share and Cite

**MDPI and ACS Style**

Hu, X.; Zak, P.J.
A Procedure to Set Prices and Select Inventory in Thinly Traded Markets Using Data from eBay. *J. Risk Financial Manag.* **2022**, *15*, 297.
https://doi.org/10.3390/jrfm15070297

**AMA Style**

Hu X, Zak PJ.
A Procedure to Set Prices and Select Inventory in Thinly Traded Markets Using Data from eBay. *Journal of Risk and Financial Management*. 2022; 15(7):297.
https://doi.org/10.3390/jrfm15070297

**Chicago/Turabian Style**

Hu, Xinbo, and Paul J. Zak.
2022. "A Procedure to Set Prices and Select Inventory in Thinly Traded Markets Using Data from eBay" *Journal of Risk and Financial Management* 15, no. 7: 297.
https://doi.org/10.3390/jrfm15070297