A consulting company estimated market demand and supply in a perfectly competitive industry and obtained the following results: where P is price,M is income,and is the price of a key input.The forecasts for the next year are = $15,000 and = $20.Average variable cost is estimated to be Total fixed cost will be $6,000 next year.Suppose that income next year is forecasted to be $10,000 instead.What will the firm's profit loss)be?

Question

A consulting company estimated market demand and supply in a perfectly competitive industry and obtained the following results:   where P is price,M is income,and  is the price of a key input.The forecasts for the next year are  = $15,000 and  = $20.Average variable cost is estimated to be  Total fixed cost will be $6,000 next year.Suppose that income next year is forecasted to be $10,000 instead.What will the firm's profit loss)be?

Quizplus · Accepted Answer

To calculate the profit, we need to find the total revenue and total cost.
Total revenue = price x quantity, where quantity is given by the demand equation. Therefore, 
TR = P(Q) = ($20 - $2($15,000))Q = ($20 - $30,000)Q = -$30,000Q

Total cost = total variable cost + total fixed cost. Total variable cost is given by the average variable cost multiplied by quantity. Therefore, 
TVC = AVC(Q) = ($2($15,000) + $0.02M + $4($11))Q = $30,300Q
TFC = $6,000

Total cost = TVC + TFC = $30,300Q + $6,000

Profit = TR - TC = -$30,000Q - $30,300Q - $6,000 = -$36,300Q - $6,000

When income is $10,000, the quantity demanded is 
Q = (11,000 - $2($15,000)) + $0.04($10,000) - $11 = - $14,400 
Since it does not make sense to have a negative quantity, the firm should shut down and incur a loss equal to the fixed costs of $6,000.

Therefore, profit = -$6,000 when income is $10,000. The change in income does not affect the calculation of the profit or loss. Thus, the answer is D.

A Consulting Company Estimated Market Demand and Supply in a Perfectly