A glass manufacturer's production function is q=〖10L〗^0.5 K^0.5(based on Hsieh, 1995). Its marginal product functions are 〖MP〗_L=〖5K〗^0.5 〖/L〗^0.5=0.5q/L and 〖MP〗_K=〖5L〗^0.5 〖/K〗^0.5=0.5q/K. Suppose that its wage, w, is $1 per hour and the rental cost of capital, r, is $4.
Draw an accurate figure showing how the glass firm minimizes its cost of production.
What is the equation of the (long-run) expansion path for a glass firm? Illustrate this path in a graph. Derive the long-run total cost curve equation as a function of q.