A4.3 Train locomotives are produced using labor and capital.

The quantities of these inputs that a firm employs determine the number of locomotives that the firm can produce. Thomas’s Trains produces locomotives according to the following production function:

Q = 3ln1L2 + 2ln1K2 where ln is the natural logarithm, Q is the quantity of locomotives produced, and L and K are the quantities of labor and capital employed, respectively.

The price of one unit of labor is wL = $15, and the price of one unit of capital is rK = $30.

a. Using the production function given above, what is the slope of the isoquant curve, dK>dL?

b. What is the slope of the isocost line, dK>dL?

c. The specific production function above means that Thomas’s Trains will always use a specific capital-to-labor ratio, K>L. Based on your answers to parts a and

b, what is the value of this capital-to-labor ratio?