3. (9 pts) Consider a producer with budget C = 200 who can buy labor L...

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3. (9 pts) Consider a producer with budget C = 200 who can buy labor L at a wage w = 10 and capital K at a price r = 5. The producer has the following production function F(K,L) = 3K 1/3 2/3 a. (2 pts) Does F(K,L) exhibit increasing, decreasing, or constant returns to scale? Show your work. Consider a new production function F(K,L) = K1/3 2/3, where is a positive constant not equal to 3. Does the new production function exhibit increasing, decreasing, or constant returns to scale? b. (2 pts) Using F(K,L) = 3K 1/3 L2/3, find the optimal bundle. Show your optimal bundle on a plot (this should include isoquant and isocost curves). c. (2 pts) Suppose the budget is reduced to C = 100 and then C = 50. Find the new optimal bundles. Plot these bundles, along with the initial optimal bundle, on one plot. Draw the expansion path. 3. (9 pts) Consider a producer with budget C = 200 who can buy labor L at a wage w = 10 and capital K at a price r = 5. The producer has the following production function F(K,L) = 3K 1/3 2/3 a. (2 pts) Does F(K,L) exhibit increasing, decreasing, or constant returns to scale? Show your work. Consider a new production function F(K,L) = K1/3 2/3, where is a positive constant not equal to 3. Does the new production function exhibit increasing, decreasing, or constant returns to scale? b. (2 pts) Using F(K,L) = 3K 1/3 L2/3, find the optimal bundle. Show your optimal bundle on a plot (this should include isoquant and isocost curves). c. (2 pts) Suppose the budget is reduced to C = 100 and then C = 50. Find the new optimal bundles. Plot these bundles, along with the initial optimal bundle, on one plot. Draw the expansion path.