In: Economics
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
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 = K0.5 + 3L0.5
On doubling the inputs:
Q' = 20.5K0.5 + 3 x 20.5 x L0.5
Q' = 20.5 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