Задача 3

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.

Решение:

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

MR`(производная)=240-80Q=0

Q=3 – точка максимума (определяется при подстановке в производную значений меньших и больших трех, при прохождение с + на – получается точка максимума)

MR=-140+240*3-40*3^2=220 д.е.

Ответ: 220 д.е.

Задача 4

Заполнить таблицу.

Q

TC

FC

VC

ATC

AFC

AVC

MC

0

50

50

0

-

-

-

-

1

90

50

40

90

50

40

40

2

120

50

70

60

25

35

30

3

150

50

100

50

16,67

33,33

30

4

200

50

150

50

12,5

37,5

50

5

270

50

220

54

10

44

70

Задача 5

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.

Решение:

Фирма прекратит производство, если P=AVCmin

AVC=VC/Q

TC=VC+FC=Q³-8Q²+20Q+50

VC=Q³-8Q²+20Q

FC=50

AVC=VC/Q=Q²-8Q+20 →MIN

AVC`=2Q-8=0

Q=4 шт. – точка минимума

AVCmin=4^2-8*4+20=4 д.е.

P= AVCmin=4 д.е.

Ответ: 4 д.е.

Задача 6

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?

Решение:

Ответ: 5 человек при заработке от 25 руб/чэ


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