Description
i'm gonna have to make a presentation as to how the problems i'm about to ask are gonna get solved as neatly and clearly as possible.
i solved these but
first off i dont if i'm right about the answers.
second off , since english is not my forte, it's pretty overwhelming just thinking about me delivering a presentation.
somehow my proffeser thinks i'm good among those students he has but actually im the other way around in reality. i 'll have my profeser check the presentation before i really do
but i don't wanna let him down by not solving these properly and neatly.
so i suggest 10 bucks per 1 question. some are pretty hard but some are pretty easy.
i'll look forward to your lovely answers
Unformatted Attachment Preview
Purchase answer to see full attachment
Explanation & Answer
Dear student,Please find enclosed a doc file with the detailed step by step solution to the four microeconomic questions.
1.
Given the utility function
𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑈(𝑥1, 𝑥2) = 2 · √𝑥1 + 𝑥2
The prices p1 = 1 and p2 = 2 and the budget line defined under the constraint U(x1,x2) = 5, we can calculate the
consumer’s minimal expenditure by considering the general minimization problem defined by
And considering the constraint that the Utility function must be 5.
The easiest way to solve this problem is by calculating the derivative of the expenditure formula and making it
equal to 0.
Considering the two variables we have, the expenditure’s formula would be:
𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 = 𝑝1𝑥1 + 𝑝2𝑥2 = 𝑥1 + 2𝑥2
Since, on the other hand, we have the constraint U(x1,x2) = 5, we can express x2 as a function of x1 by
rearranging the utility’s function equation:
𝑈(𝑥1, 𝑥2) = 2 · √𝑥1 + 𝑥2
Such that
𝑥2 = 𝑈(𝑥1, 𝑥2) − 2 · √𝑥1 = 5 − 2 · √𝑥1
If we substitute this expression into the expenditure formula, we obtain:
𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 = 𝑥1 + 2(5 − 2 · √𝑥1) = 𝑥1 + 10 − 4√𝑥1
As explained, the trick now to minimize the expenditure is to calculate the x1 value for which the derivative is
equal to 0. Thus, the first step is to derive this equation in terms of x1:
𝑑(𝑥1 + 10 − 4√𝑥1)
1
2
=1−4·
=1−
𝑑𝑥1
2√𝑥1
√𝑥1
Making this equation equal to 0, we find:
√𝑥1 = 2, 𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑥1 = 4
Substituting into the formula for x2 derived from the utility function we find,
𝑥2 = 𝑈(𝑥1, 𝑥2) − 2 · √𝑥1 = 5 − 2 · 2 = 1
Thus, taking this into account, the minimal expenditure bundle (x1,x2) is (4,1).
2.
a)
In a decreasing return to scale, we should obtain less than doubled the production output if we double the
production inputs. Thus, in order to verify that the firm is producing under a decreasing return to scale scheme,
we need to double the values of y1 and y2 and calculate the new output function q. Thus,
1
1
1
1
1 1
𝑞 ′ = 3 ∗ (2𝑦1)3 ∗ (2𝑦2)6 = 3 ∗ (𝑦1)3 ∗ (𝑦2)6 ∗ 23+6 = 𝑞 ∗ √2
Since the square root of 2 is lower than 2, then the firm is operating under a decreasing return to scale scheme,
as we wa...
Review
Review
