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Фирма, находясь в условиях совершенной конкуренции, имеет функцию общих затрат ТС=140+10Q+40Q2. При каком выпуске прибыль фирмы будет максимальна, если цена установилась на уровне 250 ден. ед.? Определить размер прибыли фирмы.
MR (прибыль)=TR(общая выручка)-TC(общие издержки)=P*Q-TC=P*Q-140-10Q-40Q^2=250Q-140-10Q-40Q^2=-140+240Q-40Q^2→max
Q=3 – точка максимума (определяется при подстановке в производную значений меньших и больших трех, при прохождение с + на – получается точка максимума)
Ответ: 220 д.е.
Конкурентная фирма имеет краткосрочные общие издержки, которые описываются как ТС=Q3-8Q2+20Q+50. Определите, при каком уровне рыночной цены конкурентная фирма прекратит производство в краткосрочном периоде.
Фирма прекратит производство, если P=AVCmin
Q=4 шт. – точка минимума
P= AVCmin=4 д.е.
Ответ: 4 д.е.
Кафе требуется обслуживающий персонал. Спрос на труд со стороны кафе описывается уравнением Ld=10 -0,2W. L – количество нанятых, W - часовая заработная плата. На объявление о найме откликнулось семь человек. Двое согласны работать при оплате от 40 руб/час, двое – от 25 руб/час, двое – от 20 руб/час, последний согласен как минимум за 15 руб/час. Определите, сколько человек будет нанянто и при каком уровне оплаты. Сколько человек наймет кафе в случае, если государство законодательно устанавливает минимальный размер оплаты труда в 40 руб/час?
Ответ: 5 человек при заработке от 25 руб/чэ
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