# Suppose inputs are only substitutable at two units of labor for every one unit of capital, and one unit of output is produced for every unit of labor or ½ unit of capital. What would be the equation for the production function? What is the average and marginal product of labor in this case?

1. Suppose inputs are only substitutable at two units of labor for every one unit of capital, and one unit of output is produced for every unit of labor or ½ unit of capital. What would be the equation for the production function? What is the average and marginal product of labor in this case?
2. Suppose output is produced according to the production function Q = M^0.5 K^0.5 L^0.5, where M is materials. Does this production function exhibit decreasing, increasing, or constant returns to scale? Show using an example.
3. Suppose output is produced according to the production function Q = min(K, L), what is the expansion path of this production function?
4. Construct a linear programming problem with two outputs and two constraints (labor and capital).