this is microeconomics. thank you for your time.

1 1. Given a production function q = SLK + 5L2 ()L3, nd the equation for the marginal product and average product of labor. Calculate the level of output, marginal product and average product of labor when L = 8 and I? = 25. 2. Given a Cobb-Douglas production function Q = K 05L0'5, nd the equation for the substitution and calculate the MRTS when (1 =2000 and L=100. 3. For the following production functions, give a thorough proof of whether it is constant, increasing or decreasing return to scale: a) q = (2L + 2100-5 b)q = 3LK2 c) q = 4L0-5 + 4K 4. A production function is said to be homogeneous of degree g if f(xL, xK) = x3f(L, K), wherex is a positive constant. For such a production function, show that the marginal product of labor and the marginal product of capital functions are homogenous of degree 3 1