require help with these two questions

Question 1 (8 points) Consider a rm with the production function, Q = K1/4L1/2. Assume that the price of one unit of capital (K) is r, the price of one unit of labor (L) is w, and the rm may sell each unit of output at price, p. a. Does this rm have decreasing, constant, or increasing returns to scale? (2 points) b. Does the rm have a convex production function, i.e., does the rms production function exhibit a diminishing technical rate of substitution? (2 points) Suppose that the rm owns a xed stock of R = 64 units of capital. It must pay 1" = 1 per unit of capital if the rm operates, Q > 0, but can avoid this cost if it chooses to shut down, Q20. Assume that W=1 and p=6. 0. Determine the prot maximizing level of output. (4 points) Question 2 (4 points) Suppose a rm has a production function y = f(:131, x2) = 121/ 2mg 2. The price of factor 1 is ml 2 16, and the price of factor 2 is mg 2 4. a. Calculate the short-run cost function when 11:1 2 fl = 4. Also, calculate the long-run cost function. (2 points) b. What are the shortrun and longrun costs of producing y = 8 units of output? (2 points)