1.Suppose a firm's production function is given by Q= 8L^0.5+ 4K^0.5. Note that for this production function, MPL = 4L^-0.5 and MPK= 2K^-0.5. Suppose "w" is the wage rate and "r" is the return to capital.

a)Determine the expression for MRTS_{L, K.} What is the shape of the isoquant?

b)Now, suppose that technological progress changes the production function to Q= 8L^0.5 + 8K^0.5. The new marginal products are given by MPL = 4L^-0.5 and MPK= 4K^-0.5. What happens to the shape of the isoquant? Explain if you expected this shape.

c)Determine the optimal capital labour ratio for both the old and the new production functions. How does this capital labour ratio change, assuming "w" and "r" are held constant. Explain if you expected this answer.

d)What should happen to "r" ceteris paribus to retain the same capital labour ratio as before the technological change?