4. A certain product has a purchase price of 80 yuan per unit and a retail price of 100 yuan per unit. To promote sales, it is proposed to give a small gift for each unit of the product purchased. Experiments show that when the gift is priced at 1 yuan, sales volume increases by 10%, and within a certain range, for every additional 1 yuan in gift value, sales volume increases by 10%. To maximize the profit from selling the product, the value of the gift should be set to \_\_\_\_\_\_ yuan (the value of the gift is always a positive integer).

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4.9 or 10 yuan.

Let the sales volume without gifts be $m$ units, and the profit when the gift is $n$ yuan be $y_{n}$ yuan. Then
$$
\begin{aligned}
y_{n} & =(100-80-n) \cdot m \cdot(1+10 \%)^{n} \\
& =m \cdot(20-n) \cdot 1 \cdot 1^{n} . \\
(0 & <n<20, n \text { is a positive integer })
\end{aligned}
$$
$(0<n<20, n$ is a positive integer)
Calculate $y_{n+1} \geqslant y_{n}$, we get
$$
m(19-n) \cdot 1 \cdot 1^{n+1} \geqslant m(20-n) \cdot 1 \cdot 1^{n} \text {. }
$$

Solving for $n \leqslant 9$. That is,
$$
y_{0}<y_{1}<y_{2}<\cdots<y_{9}=y_{10} \text {. }
$$

Therefore, the value of the gift should be 9 or 10 yuan.