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Problem 2 Nlr. Lee runs an orange grove, SmtOmnge. It's harvest season and each week using labor services (L) and equipment (K) SmtOmnge can bring q(L,K) = 250L1/3 K1/3 pounds of oranges to market. a) Does technology at SWtOmnge display diminishing returns to labor? Does it display diminishing returns to equipment? Explain. 13) Does technology at SweetOmxge display increasing, constant, or decreasing returns to scale? c) If SmtOmnge employs 2 workers and uses 3 pieces of equipment, what is the rm's Marginal Rate of Technical Substitution? What is the economic interpretation of this number? This week, labor hands cost $100 each while renting equipment costs $100 per piece and SweetOrange Wishes to produce 1,000 pounds of oranges at the lowest cost possible. d) Write 5' 1112310112113! 5 cost minimization problem, and using the Lagrangian method, nd the cheapest technique that allows SweetOrange to produce 1,000 pounds of oranges. d.1) Write the Lagrangian anction d2) Write the rst order conditions for the Lagrangian problem. d.3) Solve the rst order conditions and nd L" and K". e) What is the lowest cost at which the company can produce 1,000 oranges? f) What share of the amount you found in part e) is represented by labor cost? What share is represented by the cost of using equipment? What relationship do you notice between these shares and the parameters in the production function? g) What is the Average Cost of a pound of oranges? h) Suppose one week SweetOmage wished to harvest four times as many oranges (q' = 4,000). What would happen to the Average Cost of a pound of oranges