Question

(i) Imagine that the wage rate (w) = 10 and cost of capital (r) = 0.1. Given this information, answer the following questions: (a) Find the slope of the isocost line. (b) What is the slope of the isoquant where it is tangent to this isocost line? (c) If the marginal product of labour used in production at this point is 50 pencils per hour, what is the marginal product of capital used

Answer 1

Solution:

i.). a.). The slope of the isocost line = $\frac{w}{r}$

w = wage rate = 10

r = cost of capital = 0.1

The slope of the isocost line = $\frac{10}{0.1} = 100$

 

b.). The slope of the isoquant is known as MRTS:

MRTS = $\frac{MP_{L} }{MP_{K}} = \frac{P_{L} }{P_{K}} = \frac{w }{r}$

Since w/r = 100, this means that the slope of the isoquant (MRTS) = 100

 

c.). MRTS = $\frac{MP_{L} }{MP_{K}}$

100 = $\frac{50 }{MP_{K}}$

100MP_K = 50

MP_K = 0.5

The marginal product of capital (MP_K) = 0.5