microeconomics homework help !!!! URGENT!!?

Question

Consider a firm operating in a competitive market and using only one factor of production. If the firm is attempting to maximize profits then we know that for any change in the input and output price, the input choice and output choice must obey the Week Axiom of Profit Maximization: Delta(p)Delta(y) - Delta(w)Delta(x) >0. where p is the price of the output good, w is the price of the input good and x & y are the amounts used and produced of the input and output goods. For each, respond true or false and give a short argument in support of your answer.
a) If the price of the input does not change, then a decrease in the price of the output implies that the firm will produce the same amount or less output.
b) If the output price of the does not change, then a decrease in the input price implies of the firm will use the same amount or more of the input.
c) If both the price of output and input increase and the firm produces less output and the firm will use more of input.

Answer 1

I hope this is of some help.

Let d= delta, then according to the WAPM we have

d(p)d(y) - d(w)d(x) > 0 or rearranging we have

(1) d(p)d(y) > d(w)d(x) in order for there to be a profit.

a) True (less output)
If the price of the input does not change then d(w) = 0 so the rhs (right-hand-side) of (1) is 0. A decrease in the price of the output means d(p) is negative and therefore d(y) must also be negative in order for (1) to hold (since a negative times a negative = a positive).

b) True
if d(p) = 0 then the lhs of (1) = 0 and therefore if d(w) is negative, (1) will hold, and profits will increase if d(x) stays the same or increases.

c) False
This is not necessarily true since it depends on how much d(p) and d(w) increase and how much d(y) decreases. For example, suppose d(y) decreases by a greater percentage than d(p) increases. Then the lhs of (1) decreases. So if d(w) increases then in order for (1) to hold, d(x) would have to decrease instead of increase.

Answer 2

I agree with Spreedog, I think that this is a post war Soviet cartoon showing Churchill as the enemy of the USSR and the heir to the now dead Nazis (you'll notice that Hitler and Goebbels are standing in Churchill's shadow) by totting a racial policy of world rule by the Anglo Saxons and threatening the USSR of cutting them off from the rest of Europe with an iron curtain. The sabre and gun and the dancing means that he is a dangerous man ready to start wars at the slightest excuse. You'll notice that the flag about the Iron curtain has what looks like a grenade on the handle to show how explosive that idea would be. This was at the time a touchy subject for the Soviets because at that time western Europe was considered by the USSR as their future territories as the Communists were extremely powerful in those countries and looked ready to take power there. So cutting the USSR from those countries was a bit like taking meat from under a hungry tiger's claws. The whole cartoon was both a political statement from the Soviet state to its citizens and readying them to see the other side as the aggressor and responsible for everything in case a new conflict started between the western world and the Soviets.

Answer 3

a) Less Output
b) More of the Input
c) Less Input