Question

Функция средней выручки фирмы AR=14-1/2Q,функция издержек АС=2+1/2Q.Какую прибыль получит фирма?

Answer 1

Решение:

ТС=AC*Q = (2+0,5Q)*Q = 2Q + 0,5Q2

MC= ТС = (2Q+0,5Q2) = 2 + Q

TR= Q * AR = Q*(14-0,5Q) = 14Q – 0,5Q2

MR=TR׳, тогдаMR = (14Q – 0,5Q2) = 14 - Q

MC= MR

2+Q = 14 - Q

2Q = 12

Q = 6

Подставляем Q = 6 в уравнение TC= 2Q + 0,5Q2

ТC= 2Q + 0,5Q2 = 2*6 + 0,52= 12 + 0,25 = 12,25 

TR= 14Q – 0,5Q2  = 14*6 – 0,52 = 84 - 0,25 = 83,75
Прибыль = TR – TC
Прибыль = 83,75 – 12,25 = 71,5.

Answer 2

Calculating the Firm's Profit

To calculate the firm's profit, we can use the following formula: Profit = Total Revenue - Total Cost

First, let's find the total revenue (TR) and total cost (TC) using the given functions: - Total Revenue (TR) = AR * Q - Total Cost (TC) = AC * Q

Given: - AR = 14 - 1/2Q - AC = 2 + 1/2Q

Substitute the given values into the formulas to find the total revenue and total cost.

Total Revenue (TR) = (14 - 1/2Q) * Q Total Cost (TC) = (2 + 1/2Q) * Q

Now, we can calculate the profit using the formula: Profit = (14 - 1/2Q) * Q - (2 + 1/2Q) * Q

Let's simplify the equation to find the firm's profit.

Profit = 14Q - (1/2)Q^2 - 2Q - (1/2)Q^2 Profit = 14Q - Q^2/2 - 2Q - Q^2/2 Profit = 14Q - 2Q - Q^2/2 - Q^2/2 Profit = 12Q - Q^2

So, the firm's profit function is P(Q) = 12Q - Q^2.

Now, we have the profit function, and we can calculate the profit for a given quantity.

If you have a specific quantity (Q) for which you want to calculate the profit, please provide that value, and I can help you find the exact profit the firm will make.