Question

Home Ene Delen Problem Set 6A: Production and Costs Names SOLUTION Do this problem set if your family name begins L.Z. (-5) In the following questions, round to two decimal places (-2). Do not use fractions. Here is the production function for Barney's Batik Blousons (BBB). Labor 1 2 3 Total Product 6 14 4 2 8 9 10 1/2. Compute the marginal product (MP) and average product (AP) values in the table below. Labor 9 Production/cost information: Each worker costs $12 to hire. In addition, Barney's Batik Blousons has total fixed costs of $30. 3/7. Complete the following table. Do not use fractions. Round to two decimal places. Total Product Total Cost ATC AVC — АЕС мс — m

Need help with Profit Maximization

Answer 1

A firm like BBB objective is to maximize their profits. In order to maximize their profit firm needs to choose that quantity where their total revenue and total cost difference is maximum.we can get the condition of profit maximization by diffrention .

Profit= TR - TC

TO MAXIMIZE PROFIT .

Derivative profit function with respect to labour

So by derivation we will get

∆TR/∆L-∆TC/∆L

To get maximum value put it zero( local maxima point)

∆TR/∆L= VALUE OF MARGINAL PRODUCT OF LABOUR ,means value of the product that is firm get due to hiring one additional labour. Denote it as VMP.

∆TC/∆L= cost of hiring an additional unit of labour,that is wage price.

So the condition of profit maximization is

VMP = W,

Also VMP = market price of good* marginal product of labour.

By following this condition we can get the profit maximization quantity and thus there profit.

because in given the question nature ,the market price and wage is given ,so we need to find Marginal product of labour to get the profit maximization quantity and profit.so changing the condition,

P*MP= W

MPL=W/P

W is given 12

MPL=12/P

A).P=1.2

putting values in condition formula,

12/1.2=10=MPL

BBB will choose that quantity of labour whose margnal product is 10 and that is 5.

And the quantity that firm will produce is 50 and the profit (TR-TC)will be -30 .{TOTAL COST ALSO INCLUDES FIXED COST OTHER THAN LABOUR COST}. firm will incurs loss of 30$. Yeah firm is not making profit but this is the minimum loss that firm have to bear if it want to produce given market price and market wage.

B). P=1.5

MPL=8(W/P)

L=6

Q=58

LOSS =15(TR-TC)

C).p=0.75

MPL=16

L=4

Q=40

Loss=48

D).p=12

MPL=1

L=10

Q=72

PROFIT=714

And by same reasoning and putting price into profit maximization condition formula,you can do the rest of this section.

NEXT SECTION

IF W INCREASE to 24 then

MPL= 24/P

A).P=12

MPL=2

L=10(because there is no quantity of labour whose MPL is 2 it is between 9 and 10 so have to between labour quantity 9 and 10 ,and it chooses labour quantity of 10 because it has more profit than labour quantity of 9).

Q= 72

Profit=624

B).p=2.4

MPL= 10

L=5

Q=50

LOSS=30

AND BY SAME REASONING YOU CAN DO REST