The invention of a new machine serves as a mobile station for receiving and accumulating packed flats of strawberries close to where they are picked, reducing workers’ time and burden of carrying full flats of strawberries. According to Rosenberg (2004), a machine- assisted crew of 15 pickers produces as much output, q*, as that of an unaided crew of 25 workers. In a 6-day, 50- hour workweek, the machine replaces 500 worker-hours. At an hourly wage cost of $ 10, a machine saves $ 5,000 per week in labor costs, or $ 130,000 over a 26-week harvesting season. The cost of machine operation and maintenance expressed as a daily rental is $ 200 or $ 1,200 for a six-day week. Thus, the net savings equal $ 3,800 per week, or $ 98,800 for 26 weeks.
a. Draw the q* isoquant assuming that only two production methods are available (pure labor and labor- machine). Label the isoquant and axes as thoroughly as possible.
b. Add an isocost line to show which technology the firm chooses (be sure to measure wage and rental costs on a comparable time basis).
c. Draw the corresponding cost curves (with and without the machine), assuming constant returns to scale, and label the curves and the axes as thoroughly as possible.