Question on level of free market wage rate and employment

In the year of 1996, the U.S. Congress raised the minimum wage from $4.25 per hour to $5.15 per hour. Some of the people suggested that a government subsidy could help employers finance the higher wage. Assume the supply of low-skilled labour is specified by

L^S= 10w

where L^S is the quantity of low-skilled labour (in millions of persons employed each year) and w is the wage rate (in dollars per hour). The demand for labour is specified by
L^D =80-10w

What will be the level of free market wage rate & employment? Assume the government sets a minimum wage of $5 per hour. How many people would be employed then?
In a free-market equilibrium, L^S = L^D. Solving out yields w = $4 and L^S = L^D = 40. If the minimum wage is $5, then L^S = 50 and L^D = 30. The number of people employed will be specified by the labour demand, thus employers will hire 30 million workers.

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