2. Cascade Enterprises has a patent on a water purifying device that is used mos

Question

2. Cascade Enterprises has a patent on a water purifying device that is used mostly by restaurants to soften and purify tap water used in cooking food and cleaning dishes. Cascade Enterprises enjoys a substantial amount of market power in this rather specialized market. In the following table, columns 1 and 2 show a portion of Cascade's production function using a single variable input labor. Quantity and labor are measured in units per month. Columns 2 and 3 show the estimated demand for Cascade's water purifier. Cascade has fixed costs each month of $2,000. Marginalevenue Marginaleroduct Xx 340 46 430 450 38 a. Calculate marginal product (MP), marginal revenue (MR), and marginal revenue product b. If Cascade Enterprises must pay a monthly wage rate of S3,000, what are the profit maximizing levels of labor employment (L), output (O), price (P), and profit ()? L* = 11. P* = If the wage rate falls to $1,400 per month, what are the profit-maximizing levels of labor employment (L*), output (Q*), price (P"), and profit (*)? c. L* = iii. P#2

Explanation / Answer

MP (nth unit) = Q (n units) - Q ((n-1) units)

TR = P x Q

MR (nth unit) = TR (n unit) - TR ((n-1) units)

MRP = MP x P

b)

wage rate = $3000

Wage rate < = MRP

L* = 5

Q* = 280

P* = $48

Profit = 280 x 48 - 5 x 3000 - 2000 = -$3560

c)

Wage rate < = MRP

L* = 8

Q* = 430

P* = $42

Profit = 430 x 42 - 8 x 1400 - 2000 = $4860

L Q P ($) MP MR ($) MRP ($) 4 200 50 5 280 48 80 3440 3840 6 340 46 60 2200 2760 7 390 44 50 1520 2200 8 430 42 40 900 1680 9 450 40 20 -60 800 10 460 38 10 -520 380

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