# Microeconomics [struggling with several tasks] require help/explanation

First of all good morning, afternoon or evening depending on your location. Currently I have just begun studying economics not a while ago out of self interest, more precisely micro economics. However, just recently I stumbled upon certain tasks and have no one to go to and ask about them. I’ve been searching about several tasks on google, and have came more than halfway. Though there are some particular ones that I have no idea how to solve. I figured analyst forums might be one of my last bets. Also my apologies if these are the wrong forums, or the tasks presented are considered “dumb” or what not. I strive to learn, so please, if somebody could help me solve them and briefly explain them to me. I would be extremely grateful.

A) Illustrate in a figure how price increases the commodity of X, that would lead to changed demand for x. Show how demand change can be decomposed into a income and substitution effect.

No answer : ~~~ Could somebody link me something simular, or illustrate it in imgur?

B) The consumer can now consume a composite combination of goods for two terms. Consumption in the first period is x1, and in the second term x2. New capability depends on consumption in period 1 and 2 and has the formula U (x1, x2). Revenues in the two periods is m1 and m2, and the commodity prices are equivalent p1 and p2. Consumers can choose to borrow or to save an amount, S, the same interest rate, R. What is consumption in period 1 and 2 for a person who either borrower or saver?

Pending answer : So I have tried to do this one on my own and I came to this, does it about look right? What else should there be done?

p1*x1 = m1 x1 = m1/p1 <= first period answer

p2*x2 = m1 x2 = m2/p2 <= second period answer

C) Show in a figure how a rate increase affects savings and consumption in the first period for a consumer borrower initially. As well as explain the basis of the income and substitution effects, and why the results are different for a consumer who chooses to save in the first period.

No answer : ~~~ Again, a link, brief explanation or illsutration would help greatly.

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A) A production function has the form y = 4v^0,25, where ‘y’ is output and ‘v’ is an input. What does this function return to scale ? Explain.

Pending answer : In my knoweledge, this should be ‘decreasing returns to scale’. Though I am not sure if I am thinking right? Could anyone explain this a bit more in depth?

B) Find an expression of factor function corresponding to the production function in a). What is the interpretation of the factor function?

Pending answer : Below is my answer, if it’s right, how should I explain the new factor function?

y = 4v^0,25 Y/4 = v^0,25 (y/4)^4 = v

C) Find the cost function if the factor price is q = 4.

Pending answer : I have used C(Y) = Q 1/A * Y formula for this one. Is it enough with 1), or should I also include 2) part?

1) C(y) = q * v => 4*(y/4)^4 = C(y)

2) 4*y^4 * 1/4^4 = C(y) = y^4/4^3 = C(y) = 1/4^3 y^4

d) Find the produced quantity that maximizes profit to the manufacturer if the price of the commodity market, p = 125.

No answer : Have no idea on what exactly to use or how to solve this one.

Hopefully I am not wasting anyones time or being a nuisance.

Best regards,

Dom