$.($i$)$ One person using a hammer will take $5$ days to nail new shingles on the roof of a $300$ m$2$ house.

$($ii$)$ Two persons using a hammer but working together $($one holds a shingle, the other swings the hammer$)$ will take $2$ days to do the same job.

$($iii$)$ One person using a nail gun will take $1$ day to do the same job.

a$.$ Calculate the labour productivity $($in m$2$ per worker per day$)$ for each of the above cases.

a$.$ Labour productivity is defined as real output per labor hour and growth in labor productivity is measured as change in this ratio over time. It is also known as workforce productivity which is defined as real economic output per labor hour. Now, we will calculate labour productivity in this step.

$($i$)$ One person using a hammer will take $5$ days to nail new shingles on the roof of a $300$m$2$ house. $[$Labour Productivity $=(300$m$2)/1*5=60$m$2$

$($ii$)$ Two persons using a hammer but working together $($one holds a shingle, the other swings the hammer$)$ will take $2$ days to do the same job.

$[$Labour Productivity $=(300$m$2)/5*2=150$m$2$

$($iii$)$ One person using a nail gun will take $1$ day to do the same job.

$[$Labour Productivity $=(300$m$2)/1*1=300$m$2$

b$.$ Calculate the $\%$ change in productivity due to method change, i$.$e$.,$ from $($i$)$ to $($ii$).$

c$.$ Calculate the $\%$ change in productivity due to using technology, i$.$e$.,$ from $($i$)$ to $($iii$).$