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Determine the returns to scale for the following production functions.
a) ? = K + 7L
b) ? = KL3
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- A12. Which of the following production functions does not feature constant returns to scale? -0.3 a) Y₁ = K0.³ L0.7 t b) Yt = 0.6Kt +0.4Lt c) Y = (Kt – 1)04L06 - d) Yt = 6Kt + 4LtConsider the production function: Q = 2K + 3L. The MRTSLK is:A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
- Find the returns to scale for the following production functions: q = K.34L.34 q = KLM q = [0.3K.5 + 0.7L.5]2 q = [min (K, 2L)]2Compute the MRTS for this production function: Y (K,L) = 2K+5L100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
- Q2. Determine the returns to scale of the following production function: Hand written plzz Y = 5K0.5 +3L0.5 (a) constant (b) increasing (c) decreasing (d) indeterminateb) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of outputnestion # 1: (20) (a) Suppose a Firm produce output using the production function Q=5KL. Wage rate for hiring labor 200 an hour and cost of using capital is 100 per hour. (i) Find out the optimal quantities of labor (L') & capital (K’) to produce 1000 unit of output?. (ii) Also show the result graphically and interpret. (b) Explain the concept of Isoquant and Isocost line in firm theory. Mathematically derive the slope of isocost line and Isoquant and interpret.
- The engineers at Morris Industries obtained the following estimate of the firm's production function: Q = F(K, L) = min {3K, 4L} How much output is produced when 2 units of labor and 5 units of capital are employed?Isoquants have a v slope and, for Cobb-Douglas production functions, are The MRTS is v and is the v of the slope of the isoquant.Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C = 8950x + 220,000, R = 9857x