A glass manufacturer's production function is q = 10L0.5K0.5 (Hsieh, 1995). Suppose that its wage, w, is $1 per hour and the rental cost of capital, r, is $4.
a. Draw an accurate figure showing how the glass firm minimizes its cost of production.
b. What is the equation of the (long-run) expansion path for a glass firm? Illustrate in a graph.
c. Derive the long-run total cost curve equation as a function of q?