Question

Initially a​ firm's wage is w = $42 and its rental cost of capital is r = $42. After its wage rate doubles, how do its isocost lines​ change?

Let L represent labor and K capital.

Graph an isocost line at the original​ wage, when the wage is w = $42. Label this line "I1"

Graph an isocost line at the new​ wage, when the wage doubles. Label this line "I2"

Answer 1

Initially a​ firm's wage is w = $42 and its rental cost of capital is r = $42.

Now, it is told that,

L represents the labor and K represents the capital.

w = price of per unit L

r = price of per unit K

Hence, if a certain level of production requires

capital = K units and labor = L units, then

Cost of Labor = w.L

Cost of Capital = r.K

Hence, Total Cost (C) of Production is

C = w.L + r.K

Now, for different combinations of (L,K), we get the same cost C at every point on the Isocost line.

Now, let us derive the isocost lines for the given levels of wage rate and rental rates.

When,

w = $42 and r = $42, the isocost line's equation would be,

C1 = 42.L + 42.K.......(1) {C1=cost level=constant}

The slope of the isocost curve is,

dK/dL = -(42/42) {as C1 is constant}

or, dK/dL = (-1)

Now, when wage rate doubles, then,

w' = $84 and r = $42 and the isocost line's equation would be

C2 = 84.L + 42.K.......(2) {C2=cost level=constant}

The slope of the isocost line is

dK/dL = -(84/42) {as C1 is constant}

or, dK/dL = (-2)

The slope of the isocost line has increased. Hence, the isocost line will become steeper now.

According to the question, the line 'l1' denotes the isocost level C1 and the line 'l2' denotes the isocost level C2. Let us draw the two lines in two diagrams below.

First let us draw 'l1' i.e.

C1=42.L+42.K

Now, let us draw 'l2' i.e.

C2=84.L+42.K

Hence, the slope of the isocost lines changes from (-1) to (-2). The isocost lines become steeper at the new wage rate.

Hope the solution is clear to you my friend.