GATE 2024 Question 61: Factor markets and income distribution

In an economy, the effort level of a worker in firm $i$ is denoted by $e_i$ and depends on the wage $W_i$ received by the worker from the firm, and the minimum wage $W_0$ set by the government. The effort function is given by

$e_i(W_i,W_0) = \sqrt{W_i-W_0}$

If the firm employs $N_i$ unit of workers, then the efficiency unit of labour employed by the firm is $e_iN_i$. The production is based only on the efficiency unit of labour, and the production function is given by

$F(e_iN_i) = \log_e(e_iN_i)$

If the minimum wage set by the government is 10, and the profit maximizing firms sell the good in a competitive market at price $P$ by choosing $W_i$ and $N_i$, then the profit maximizing wage set by the firm will be ______ (rounded off to one decimal place).