Question

K Isoquant: Q 70 Tangency 8 Isocost: TC - $? 10 Figure 1. Isoquant and Isocost Price of L = $20; Price of K ? ; TC ?

Answer 1

(A) X-axis intercept of the isocost line is 10.

Isocost line X-axis intercept = TC/ Price of L (Note: Labor is measured on the X-axis)

10 = TC / Price of L

TC = (10) (Price of L)

TC = (10) ($20)

TC = $200

Isocost line equation: TC = (L) (Price of L) + (K) (Price of K)

At tangent point, K =8 and L=6.

TC = (L) (Price of L) + (K) (Price of K)

$200 = (6) ($20) + (8) (Price of K)

$200 = $120 + (8) (Price of K)

(8) (Price of K) = $200 - $120

(8) (Price of K) = $80

Price of K = $80/8

Price of K = $10.

Isocost line Y-axis intercept = TC/ Price of K (Note: Capital is measured on the Y-axis)

Isocost line Y-axis intercept = $200 / $10

Isocost line Y-axis intercept = 20

(B) If the price of capital increases while the price of labor is unchanged, the isocost line rotates inwards on the Y-axis (where capital is measured).  In this case, in order to produce Q=70 with the original total cost, the manager must hire more labor, because now capital is expensive than earlier and to produce same amount of output with the same total cost, the firm has to substitute capital with labor. Hence, labor will increase and capital will decrease.

Answer: Option (D)