Suppose that the production function for Hannah and Sam’s home remodeling business is Q = F(L, K) = 10L0.2K0.3. If the wage rate is $1,500 per week and the cost of renting a unit of capital is $1,000 per week, what is the least-cost input combination for remodeling 100 square feet each week? What is the total cost? [HINT: We did a similar problem in class. Also, you need to use the fact that under the given production function, MRTSLK = 2K/3L.]
Consider the data given in the problem above and assume that Hannah and Sam are currently remodeling 200 square feet each week. That is, their capital stock is fixed at the level that corresponds to the cost minimizing input combination for remodeling 200 square feet each week. And capital stock cannot be changed in short run while labor is completely variable. What is their short-run and long-run cost function?