Suppose that a company's production process corresponds to the following production function:Q=L^0.8K^0.2. Also assume that the wage rate (W) is $1 and the rental cost of capital (r) is $4. For this production function, the MP_L= 0.8L^-0.2K^0.2and the MP_K= 0.2L^0.8K^-0.8.

1.

Derive the equation of the long-run expansion path.Make sure to show all your work.

2.

Draw the diagram of the long-run expansion path that corresponds to the equation derived in part a) going through three different cost-minimizing input bundles. What is the value of the slope along this curve?K on the vertical axis an(d L on the horizontal axis. Clearly label each curve.(Hint: In total you should have seven curves: three isocost lines, three isoquants, and one long-run expansion path curve.)

3.

Derive the long-run cost equation as a function of Q.Make sure to show all your work.

4.

Draw the diagram of the long-run cost curve that corresponds to the equation derived in part c). What is the value of the slope along this curve?TC on the vertical axis and Q on the horizontal axis.