Question

In: Economics

1. If total cost is given by TC = 500+ 10Q − 10Q2 + 0.5Q3 ,...

1. If total cost is given by TC = 500+ 10Q − 10Q2 + 0.5Q3 , then average variable cost is minimized at __________ units of output.

a. 20 b. 10 c. 50 d. 5 e. 100

12. If output is produced according to Q = K0.5 + 3L0.5, then this production process exhibits:

a. increasing returns to scale b. constant returns to scale c. decreasing returns to scale d. first decreasing and then increasing returns to scale e. first increasing and then decreasing returns to scale

13. Company XYZ has zero fixed costs and its average variable cost of cases is given by AVC = 5Q + 600, the marginal cost at an output level of 15 units is:

a. $625 b. $500 c. $750 d. $600 e. $550

14. Given a cost function C(Q) = 400 + 18Q + 6Q2 , what is the marginal cost function?

a. 18 + 12Q. b. 18 + 12Q2. c. 400 + 6Q2. d. 18Q + 6Q2

Solutions

Expert Solution

Answer:

Question1]

Total cost(TC) = 500 + 10Q -10Q² + 0.5Q³

Average cost is found by dividing the total cost by Q units

Average cost(AC) = TC / Q = 10 - 10Q + 0.5Q²

Taking the first derivative of the average cost function

d(AC)/dQ = -10 + Q

Taking the second derivative of the above equation

d²(AC)/dq² = 1

Hence the above function satisfies the conditions of minimum

Equating the first derivative to zero

-10 + Q = 0

Q = 10 units

Hence the average cost is minimized at 10 units

B] 10 units is correct answer.

Question2]

If output is produced according to Q = K0.5 + 3L0.5, then this production process exhibits:

C] decreasing returns to scale

Explanation:

Q = K^0.5 + 3L^0.5

On doubling the inputs:

Q' = 2^0.5K^0.5 + 3 x 2^0.5 x L^0.5

Q' = 2^0.5 x Q

Output less than doubles. Therefore, there exist decreasing returns to scale.

Question3]

AVC = 5Q + 600

TVC = AVC * Q = (5Q + 600) * Q = 5Q² + 600Q

MC = dTVC/dQ = d(5Q² + 600Q)/dQ = 10Q + 600

Calculate the marginal cost when output is 15 units -

MC = 10Q + 600

MC = (10*15) + 600 = 750

The marginal cost at an output level of 15 units is $750.

Hence, the correct answer is the option (c)$750.

Question4]

Marginal Cost is the change in total cost and a change in function found by differentiation
MC=dTC/dQ=18+12Q
MC=18+12Q

Correct option A] 18 + 12Q

Rahul Sunny answered 1 year ago

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