Question

Note 1: Show all of your work in order to receive full credit. Note 2: Assume that there are no intermediate inputs such that VASH ignore VASH in your calculations) Note 3: Round all answers to 2 decimal places. 1 (in other words, you can Assume that the production function for producing lettuce without the mechanical lettuce harvester is: Q-.5937L 7K3 Assume that the production function for producing lettuce with the mechanical lettuce harvester is: For problems 1-4 assume that the wage for farmworkers is $12, the price of lettuce is equal to $10 per box, and that Fran produces 50 boxes of lettuce per year. Fran recently found a used mechanical lettuce harvester on a reputable farm equipment company's website that is on sale for $3074.50. In order for Fran to buy the mechanical harvester, she will have to borrow the $3074.50 from an agricultural bank (i.e., L 3074.50). The bank has decided to give Fran a loan and has offered to finance the loan overa 30 year period (ie. T-30) at an annual interest rate of 5% (i.e., r = .05). Fran has a limited annual budget and has decided that, if she takes the loan, she would like to make equal annual payments over the life of the loan. We denote Fran's 30 equal annual payments to the bank as "C." Fran will not have to make the annual payments if she decides not to purchase the mechanical harvester. The amount of capital used without using a mechanical harvester is K1 1000, and the amount of capital used with a mechanical harvester is K2 -1500. Problems 1 and 2 are worth 10 points each. Each subpart of question 3 is worth 10 points. Problem 4 is worth 10 points and problem 5 is worth 15 points. Derive the optimal labor demand when Fran does not purchase or use a mechanical lettuce harvester. 1. How much annual profit does Fran make without the mechanical harvester? Note: We have introduced 2. the cost of capital into this problem such that the new profit function is: π-pQ-wL-rK-C 3. a. Derive the optimal labor demand when Fran uses the mechanical harvester to produce lettuce. b. Show graphically what happens in a labor market when Fran chooses to use the mechanical harvester. c. Does the scenario you depicted in question 3b reinforce your answers from questions 1 and 3a? Why or why not?

Answer 1

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686.25 Anomt 30c 686.25 se 989t 56. 20833 te omoint faid for a0yeor) orth at meahanical harvegt =lo00 SoLaber eaal to (L (oo SD 93 .9493) Cto. Ge235/ Profit doa fran mate asithout mechanical haxvelt PQ-wL-rk-c Cgan)

3 hen by T Pa-wL- Yk - c - Cta) Ca /64 C0.o5oo0) as. 833. 349 97-856- 5o-256. 2o833 -S00- Profit b8981 2S L =