Maurice has the following utility function: U (X Y) =20X+80Y-X^2-2Y^2, where X is his consumption of CDs with a price of $11 an
1 answer:
Answer:
1 CD and 19 movie videos
Explanation:
This is a quadratic programming problem. Given the utility function, product price and budget constraint. the following relation between X and Y is:
When that is inserted in the utility function, the function is:
In order to find the maximization parameter X, the first derivative of the function is needed (leveled with zero), and it is:
The value for X is 1,06 which can be rounded to 1. From the first relation, we see that Y is 19.
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Answer:
a) Average price per unit = 700
b) average marginal cost = -1.5 dollars/frame
c) For 201 frames are produced = $698.5
Explanation:
Given Data:
C(x) = 60000 + 400x
a) Average cost for 200 units:
Total Cost of 200 units will be:
C(200) = 60000 + 400(200)
C(200) = 140,000
Total Cost of 200 units = 140,000
Average price per unit = Total Cost / number of units
Average price per unit = 140,000/200
Average price per unit = 700
b) Marginal Average Cost:
We know that marginal cost = (x)
And the average marginal cost =
So,
= the derivative of ()
= the derivative of ()
= + 0
So,
average marginal cost =
at x = 200 units
average marginal cost =
average marginal cost = -1.5 dollars/frame
c) Average cost per frame if 201 frames are produced:
We already seen in the part b that, the average marginal cost is decreasing by 1.5 dollars /frame. So,
if 201 frames are produced the instead of 200 then the difference is of 1 frame and we discussed that average marginal cost of 1 frame is decreasing at 1.5 dollars per frame.
So,
As we know the average cost from part a = 700 dollars.
Therefore, for 201 item = 700 dollars -1.5 dollars
For 201 frames are produced = $698.5