Answer to Question #83441 in Microeconomics for parii

Question

4. Suppose Fraser Forest is the only employer for lumberjacks in a small town. Every
lumberjack can cut one tree per hour, and Fraser Forest sells each tree for $100. At
an hourly wage w, 20(w-10) lumberjacks are willing to work (nobody wants to
work for less than $10/hour). Assume that labour is the firm’s only cost.
a) How many lumberjacks will the firm hire? What is the wage rate paid by the
firm? Draw a graph to show your answer.
b) What is the firm’s profit (per hour)?
Now suppose there are many small firms hiring lumberjacks. Lumber price and
labour supply are the same as before.
c) How many lumberjacks will be hired in equilibrium? What is the wage rate paid
to each lumberjack in equilibrium? Draw a graph to show your answer.
d) What is each firm’s profit (per hour)?

Answer 1

4. Every lumberjack can cut one tree per hour, and Fraser Forest sells each tree for $100. At

an hourly wage w, 20(w-10) lumberjacks are willing to work.

a) The quantity produced equals to the number of workers hired, so Q = N = 20(w - 10), so the total profit of this firm is:

TP = 100*20(w - 10) - w*20(w - 10) = (2000 - 20w)*(w - 10) = 2000w - 20w^2 - 20000 + 200w = -20w^2 + 2200w - 20000.

TP is maximized, when TP' = 0, so:

(-20w^2 + 2200w - 20000)' = 0,

40w = 2200,

w = $55,

Q = N = 20(55 - 10) = 900.

b) The firm’s profit (per hour) is:

TP = TR - TC = 100*900 - 55*900 = $40500.

If there are many small firms hiring lumberjacks and lumber price and

labour supply are the same as before, then:

c) The number of lumberjacks will be hired in equilibrium is:

Q = 20(w - 10) = 100,

w = $15,

d) Each firm’s profit (per hour) is TP = 100*100 - 100*15 = $8500.