Question

Consider a firm facing a Cobb-Douglas production function with two inputs, labor and capital. Suppose that cost of capital is double the wage rate. What is the slope of the firm’s isocost curve? (Your answer must be a number.)

Answer 1

Isocost line is given by :

wL + rK = C where w = wage rate, L = Labor units, K = amount of capital, r = cost of capital = 2w and C = Cost(Note for each isocost we have fixed C)

Considering K on vertical axis and L on horizontal axis.

Slope of isocost = dK/dL

Now we have : wL + rK = C => wL + 2wK = C

Differentiating both sides with respect to L we get :

w(dL/dL) + 2w(dK/dL) = 0(Note for each isocost we have fixed C)

=> dK/dL = -w/(2w) = -0.5

Hence, Slope of isocost line = -0.5(Negative sign means that Isocost curve is downward sloping)