Question

In: Economics

QUESTION 3 A firm's production function is Q = 2 KL, with MP L = 2K...

QUESTION 3

A firm's production function is Q = 2 KL, with MP L = 2K and MP K = 2L. The wage rate is $4 per hour, and the rental rate of capital is $5 per hour. If the firm wishes to produce 100 units of output in the long run, how many units of K and L should it employ?

a.

K = 6.33; L = 7.91.
b.

K = 2; L = 2.
c.

K = 4; L = 5.
d.

K = 5.21; L = 6.45.

QUESTION 4

If TC = Q3 - 20 Q2 + 220 Q, and MC = 3Q 2- 40Q + 220, then there are economies of scale until the level of output reaches:

a.

5.
b.

0.
c.

10.
d.

15.

QUESTION 6

Diseconomies of scale exist when:

a. average total cost is minimized.
b. marginal cost is increasing.
c. average total cost is increasing.
d. average total cost is decreasing.

Solutions

Expert Solution

Question 3:

Q = 2 KL

MP L = 2K and MP K = 2L

Wage rate= W= 4

Rental rate of capital= r= 5

To find how much of K and L must employ:

MP L / MP K = W/r

2K/2L= 4/5

5K= 4L

L= (5/4)K Demand for L

If Q= 100:

100= 2KL

Use L=(5/4)K:

100= 2K(5/4)K

100 x (2/5)= K2

40 = K2

K= (40)1/2 = 6.33

Use K=6.33 in L=(5/4)K:

L= (5/4)6.33= 7.91

Option a is the correct answer.

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Economies of scale arises where average cost is decreasing and diseconomies of scale arises when average cost is increasing.

Average cost will decrease until a point at which it reaches lowest point. Lowest point of Average cost arises where:

Average cost = MC

Question 4:

TC = Q3 - 20 Q2 + 220 Q

MC = 3Q2 - 40Q + 220

Average cost= TC/Q= Q2 -20Q+220

To find out the point till which average cost is decreasing:

MC= Average cost

3Q2 - 40Q + 220 = Q2 -20Q+220

3Q2 - 40Q + 220 -Q2 +20Q-220=0

2Q2 - 20Q =0

2Q(Q-10)= 0

Q = 0 or 10

There are economies of scale until the level of output reaches 10.

Option C is the correct answer.

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Question 6:

Economies of scale arises where average cost is decreasing and diseconomies of scale arises when average cost is increasing.

Correct option is:

c. average total cost is increasing.

Rahul Sunny answered 1 year ago
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