Question

The supply function for good X is given by Q x s = 200 + 4P X - 3P Y - 5P W, where P X is the price of X, P Y is the price of good Y and P W is the price of input W. If P X = 500, P Y = 250, P W = 30, then the supply curve is:

Please solve step by step. I think the answer is -700+4Px, but to get that the numbers are plugged in except 500. Why is that the case??

Answer 1

Supply function gives us the quantity supplied by a firm of any good and service at a particular time, given the various price level it faces.

Note that, as the price of the good or service in question increases, the firm will want to produce more because they can earn higher profits by selling them at the higher price. Hence, there is a direct relationship beween price of a good/service and it's supply.

Also remember, when we try to derive the supply curve, we try to find the various levels of quantity supplied (or, produced) by the firm when it faces different prices. So, given a level of price, we try to see the corresponding supply.

So, supply curve is always a function of price of the good/service in question.

Note that, here, we are looking at the supply function of X. Hence, it will be a function of price of X, which is Px

So, initially, we are given the supply function as:

where

Px is price of X

Py is price of good Y

Pw is the price of input W

We are also given the values of Px=500, Py=250 and Pw=30

As I have told you that supply curve is a function of price of the good in question (here, function of price of X , i.e. function of Px), so we will keep Px as it is in the supply function, while substitute the values of other prices (i.e. we will substitute Py and Pw values in the supply function)

Hence, supply function was:

put the values Py=250 and Pw=30. We get,

or,

or,

or,

This is the equation of the supply curve. Note that we have kept this as a fucntion of Px. So for various values of Px, we can determine the corresponding value of Qxs (the quantity supplied)

Hope this helps!! Give a thumbs up if you liked my answer and if there are doubts, comment below so that I can help you! :)