A cost minimising firm has labour as its only input, but labour has two components, the number of workers, N, and hours per worker, h. Each worker hired incurs fixed costs (i.e. costs that do not vary with output), f, while the wage for “standard hours” (hours 3 up to and including 40 hours per week) is w per hour. For hours above 40 the firm must pay its workers an overtime premium of 50 percent, i.e. 1.5w. a) Derive the firm’s isolabour function (the function showing combinations of N and h which generate the same overall employee-hours). b) Derive the firm’s isocost function (the function showing combinations of N and h which generate the same total cost of labour). [HINT: it will have two “segments”, one for less than 40 hours per week and one for more than 40 hours per week.] c) Sketch the isolabour and isocost functions (with N on the y-axis and h on the x-axis). [HINT: to be able to show the isocost curve and know its shape, it helps to find out how its slope changes at the threshold of 40 hours per week…]
A cost minimising firm has labour as its only input, but labour has two components, the number of workers, N, and hours per worker, h. Each worker hired incurs fixed costs (i.e. costs that do not vary with output), f, while the wage for “standard hours” (hours 3 up to and including 40 hours per week) is w per hour. For hours above 40 the firm must pay its workers an overtime premium of 50 percent, i.e. 1.5w. a) Derive the firm’s isolabour function (the function showing combinations of N and h which generate the same overall employee-hours). b) Derive the firm’s isocost function (the function showing combinations of N and h which generate the same total cost of labour). [HINT: it will have two “segments”, one for less than 40 hours per week and one for more than 40 hours per week.] c) Sketch the isolabour and isocost functions (with N on the y-axis and h on the x-axis). [HINT: to be able to show the isocost curve and know its shape, it helps to find out how its slope changes at the threshold of 40 hours per week…] d) Explain, intuitively and graphically, the effect of an increase in f on the optimal choice of hours per worker and the number of workers hired. [HINT: to see what happens to the shape of the isocost curve, it helps to calculate how the slope of the isocost curve changes when f changes.] e) Explain, intuitively and graphically, the effect of an increase in the overtime premium on the optimal choice of hours per worker and the number of workers hired.
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