A manufactures production function in the long run (based on Hsieh, 1995) is expressed as =(,)=100.50.5 Its marginal product functions are = 0.5 , and = 0.5 . Suppose the wage, , is $1 per hour and the rental cost of capital, , is $4.

a. What is the cost minimizing ratio of labor and capital for this firm?

b. If the firm chooses to produce = 100, how much labor and capital will it employ?

c. Draw an accurate figure showing how the glass firm minimizes its costs of production?

d. What is the equation of the long run expansion path? Illustrate this path in the graph above.

e. Derive the long run cost curve as a function of output ().