Question

Frankie produces computer software. His firm's production function is Q = 1K + 2L, where Q is the programs, K is capital employed, and L is the labor used. If Frankie faces factor prices of Pk=5 and Pl =5, the cheapest way to produce Q = 90 is:

Part 1: By using how many units of capital? ____________

Part 2: By using how many units of labor? ____________

If Frankie faces factor prices of Pk=7 and Pl=21, the cheapest way to produce Q = 90 is

Part 3: By using how many units of capital? ____________

Part 4: By using how many units of labor? ____________

Answer 1

We have the production function Q = 1K + 2L. MRTS = MPL/MPK = 2/1 = 2. Price ratio PL/PK = 5/5 = 1. Since MRTS > PL/PK, we should use only Labor and no capital. This implies that the production function is Q = 2L

Part 1) Capital = 0

Part 2) Labor = 90/2 = 45 units

Now MRTS = MPL/MPK = 2/1 = 2. Price ratio PL/PK = 21/7 = 3. Since MRTS < PL/PK, we should use no Labor and only capital. This implies that the production function is Q = K

Part 3) Capital = 90/1 = 90 units

Part 4) Labor = 90/2 = 0 units