Question

uestions 0 4 in your answers, if needed. Calculation Q 2- Note: with respe (a) Are X nuts with a monthly demand n120+0.00102, where P is (20 points) An farm produces premium organic macadamia nuts with a month function ofa-15.000-500P, and total cost function TC-4,000+ 12Q + 0.001g、whe the price of macadamia nuts per pound and Q is quantity (pounds). (b) S (a) What are the optimal quantity, price, and profit of the company? (b) Now suppose the farm were to cut down part-time employees without losing the productivity, which reduces their cost of hiring by $3,000 per month. What are theo quantity, price, and profit under the new condition? ptimal

Answer 1

1. a) Optimal condition; MR = MC

Q = 15000 - 500P

P = (15000 - Q)/500 = 30 - Q/500

TR = PQ = 30Q - Q²/500

MR = 30 - 2Q/500

TC = 4000 + 12Q + 0.001Q²

MC = 12 + 0.002Q

MR = MC

30 - 0.004Q = 12 + 0.002Q

30 - 12 = 0.006Q

18 = 0.006Q

Q = 18/0.006

Q = 3000 units

P = 30 - 3000/500 = 30 - 6

P = 24

Profit = TR - TC = PQ - (4000 + 12Q + 0.001Q²)

Profit = 24 x 3000 - 4000 - 12(3000) - 0.001(3000)²

Profit = 72000 - 4000 - 36000 - 9000

Profit = 23000

b) TC = 4000 + 12Q + 0.001Q² - 3000 = 1000 + 12Q + 0.001Q²

MC= 12 + 0.002Q

MR = 30 - 2Q/500

Equilibrium MR = MC

we get P = 24 and Q = 3000

Profit = PQ - (1000 + 12Q + 0.001Q²) = 24 x 3000 - 1000 - 12(3000) - 0.001(3000)²

Profit = 72000 - 1000 - 36000 - 9000 = 26000