Question

janetta produces bratwurst using two inputs, labor and capital. her production process has the production function q=2l^0.5k^0.5, assume she wants to produce q=1500, price for labor is 15,price of capital is 30. write out the equation for the isocost curve that janetta faces

Answer 1

Cost is minimized when (MPl / MPk) = w/r = 15/30 = 1/2

MPl = q/l = 2 x 0.5 x (k/l)^0.5

MPl = q/l = 2 x 0.5 x (l/k)^0.5

MPl/MPk = k/l = 1/2

l = 2k

Substituting in production function with q = 1500,

2 x (2k)^0.5 x l^0.5 = 1500

2^0.5 x l^0.5 x l^0.5 = 750

l = 530.33

k = l/2 = 265.17

Total cost (C) = wl + rk = 15 x 530.33 + 30 x 265.17 = 7954.95 + 7954.95 = 15909.9

So,

Equation of isocost line:

15909.9 = 15l + 30k