Lone Star Industries offers online automobile Insurance to preferred risk driver

Question

Lone Star Industries offers online automobile Insurance to preferred risk drivers in the state of Texas. The company is the low cost provider of insurance in the market with fixed costs of $18 million per year, plus variable costs of $750 for each driver insured on an annual basis. Price and marginal revenue functions for the company are as follows P = $1,500 - $.005Q MR = $1,500 - $.01Q 1. Calculate the company’s MC function, 2. Calculate the profit maximizing activity level 3. Calculate the company’s optimal profit and return on sales.

Explanation / Answer

Given: fixed costs ,= $18 million, Average Variable costs = $750 per driver, P = $1,500 - $.005Q, MR = $1,500 - $.01Q

1. Calculate the company’s MC function

Total cost = Total Fixed cost + Total variable cost

TC = $18 million + 750Q and MC = 750

2. Calculate the profit maximizing activity level

profit maximizing activity level is at point where MC = MR

MR = $1,500 - $.01Q = $750, so Q = 75000

3. Calculate the company’s optimal profit and return on sales.

Profit = TR - TC, where TR = P*Q = (1500 - 0.005(75000))75000 and TC = $18 million + 750(75000)

Profit = 84375000 - 74250000 = 10125000

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