Sunflower Inc. is a major supplier of reverse osmosis and ultrafiltration equipm

Question

Sunflower Inc. is a major supplier of reverse osmosis and ultrafiltration equipment, which helps industrial and commerical customers achieve improved production processes and a cleaner work environment.   The company has recently introduced a new line of ceramic.filters that enjoy patient protection. Relevant cost and revenue relations for this product are as follows:

P = 300 -0.001Q

TC= 900,000 + 20Q + 0.004Q2

Where P is Price Q is output, and TC is total cost

A. Compute Sunflower's optimal price/ output combination.

B. Compute firm's TR, TC, and profit using the price and quantity you calculated in part A.

Explanation / Answer

(A) Calculate Sunflower's optimal price/output combination -

P = 300 - 0.001Q

Calculate Total Revenue -

TR = P*Q

     = (300 - 0.001Q)Q

     = 300Q - 0.001Q2

Calculate Marginal Revenue -

MR = dTR/dQ = d(300Q - 0.001Q2 )/dQ = 300 - 0.002Q

TC = 900,000 + 20Q + 0.004Q2

Calculate Marginal Cost -

MC = dTC/dQ = d(900,000 + 20Q + 0.004Q2)/dQ = 20 + 0.008Q

The optimal output level of a firm is that output level at which marginal cost equals marginal revenue.

Equating marginal revenue and marginal cost to determine optimal output level -

MR = MC

300 - 0.002Q = 20 + 0.008Q

-0.002Q - 0.008Q = 20 - 300

0.010Q = 280

Q = 28,000 units

The optimal output of Sunflower Inc. is 28,000 ceramic filters.

Calculate optimal price -

P = 300 - 0.001Q = 300 - 0.001*28,000 = 300 - 28 = 272

The optimal price of Sunflower Inc. is $272 per ceramic filter.

(B) Calculate Total Revenue (TR) -

TR = 300Q - 0.001Q2 = 300*28,000 - 0.001(28,000)2 = $7,616,000

The firm's total revenue is $7,616,000.

Calculate Total Cost (TC) -

TC = 900,000 + 20Q + 0.004Q2 = 900,000 + 20*28,000 + 0.004*(28,000)2 = $4,596,000

The firm's total cost is $4,596,000.

Calculate Profit -

Profit = TR - TC = $7,616,000 - $4,596,000 = $3,020,000

The firm's profit is $3,020,000.

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