economics question

Question

A consumer will be on a ___ indifference curve with a conditional grant than with an unconditional grant. A. higher B. lower C. the same D. none of the above

The production function for a firm is given by TP = 4K²L². The price of capital is $4 and the price of labour is $2. The budget is $100.

The optimal amount of capital is:

1. A. 25
2. B. 12.5
3. C. 8
4. D. 4

The production function for a firm is given by TP = 4K²L². The price of capital is $4 and the price of labour is $2. The budget is $100.

The optimal amount of capital is:

1. A. 25
2. B. 12.5
3. C. 8
4. D. 4

The production function for a firm is given by TP = 4K²L². The price of capital is $4 and the price of labour is $2. The budget is $100. The optimal amount of labour is:

1. A. 4
2. B. 8
3. C. 12.5
4. D. 25

The production function for a firm is given by TP = 4K²L². The price of capital is $4 and the price of labour is $2. The budget is $100. The maximum output is:

1. A. 100015
2. B. 230925
3. C. 340925
4. D. 390625

Production managers for a manufacturing firm estimate their production function to be:

TP = 24L +10.5L² - L³

where TP is the output and L is labour. The price of a unit on output is $20.

At what level of input do diminishing returns occur?

1. A. L=5.25
2. B. L=3.5
3. C. L=8
4. D. L=1

Production managers for a manufacturing firm estimate their production function to be: TP = 24L +10.5L2 - L3 where TP is the output and L is labour. The price of a unit on output is $20. At what level of input does average product peak?

1. A. L=3.5
2. B. L=5.25
3. C. L=8
4. D. L=1

Production managers for a manufacturing firm estimate their production function to be: TP = 24L +10.5L2 - L3 where TP is the output and L is labour. The price of a unit on output is $20. What is the maximum output that can be produced?

1. A. L=3.5
2. B. L=5.25
3. C. L=1
4. D. L=8

Production managers for a manufacturing firm estimate their production function to be: TP = 24L +10.5L2 - L3 where TP is the output and L is labour. The price of a unit on output is $20. What is the maximum is dollars that you would pay for 5 labour?

1. A. $100
2. B. $1030
3. C. $5150
4. D. $1080

Economies of scale can be due to:

1. A. volume purchasing
2. B. higher borrowing rates
3. C. higher wage rates
4. D. all of the above

Diseconomies of scale can be due to:

1. A. Division of labour
2. B. Labour saving technology
3. C. Cheaper borrowing rates
4. D. More regulation

Answer 1

Consumer will be on a lower indifference curve with a conditional grant than an unconditional grant, unless by major coincidence the conditional grant exactly matched what the consumer would have bought anyway.

Price of capital is $4

Price of labor is $2

Production = 4K^2L^2

budget is $100L

4K + 2L =100

2K + L = 50

L= 50-2K

Spend it all on either K or L and production = 0

spend it on somewhere in the middle, and production is maximized

Labor can be utilized at from 0 to 50. In the middle is 25

Capital can be utilized at from 0 to 25, in the middle is 12.5

Those are the maximum production use of labor and capital within the budget of $100

Total product = TP=4K^2L^2 = 4(KL)^2 = 4(K(50-2K)^2 = 4(50K-2K^2)^2

4(2500K^2 -200K^3 +4K^4)= 4K^2(2500-200K+4K^2)

Take the derivative, set it = 0 and solve for K

Okay, that's getting tediously unnecessarily complicated, although you could grind out the answer that way.

It's easiest to just maximize KL = K(50-2K) since that automatically maximizes its square times 4

take the derivative, set = 0, and solve for K

(KL)' = (50K-2K^2)' = 50-4K =0

25-2K = 0

2K =25

K = 12 1/2

L=50-2K = 50 -25= 25

K= 12.5, L= 25

If you want to know the maximum production level

plug L=25 and K=12.5 into TP = 4(K)^2(L^2)

= 4(12.5)^2(25)^2

= 4(156.25)(625)

=625)(625)= 625^2 =390,625

to check that, you might try slightly more and slightly less than K=12.5

such as K=13, L=50-2K=24

and K=12, L=50-2K = 26

Plug those into the total production equation and you should get

slightly less than 300,625 for each. K=12.5 with L=25 is the most efficient allocation of resources when the budge is 100, with prices 4 and 2, and a production function of 4(K^2)(L^2)