Currently,
,where MPs and MPa are the marginal products of steel and aluminum for a company whose production function is Q = s0.5 a0.5. Ps = Pa = $1 are the prices of steel and aluminum, respectively, and the company has a total budget of $2 to spend on these inputs. If the market price of the output is $3 per unit, then how many units of s and a should the firm hire? What will be its output, revenue, costs, and profits?
What will be an ideal response?
We know that the budget line has to satisfy the following condition:
TC = Ps.s + Pa.a or for the given information,
2 = 1.s + 1.a, or 2 = s + a.
Now the equilibrium condition tells us that we have to satisfy
,
which can be written as
,
or from the given information this amounts to
,
which when simplified gives us the condition
s = a. This can be substituted in the budget line equation above:
2 = s + a or
2 = s + s or
2 = 2 s or
s = a = 1 unit.
This tells us that output produced is Q = s0.5 a0.5 = (1)0.5 (1)0.5 = 1 unit.
Total Revenue = market price times quantity produced = $3 x 1 = $3.
Total Cost = $2 -the amount we have to spend.
Profits = Total Revenue -Total Cost = $3 - $2 = $1.
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