A firm has a supply function given by S(p)=4 p. Its fixed costs are 100 . If the price changes f

step 1 Okay, so we're basically going to be looking at this question. We are given a supply function, w

A firm has a supply function given by S(p)=4 p. Its fixed...

Key Concepts

Comparative Statics

Comparative statics is an analytical method used in economics to study how a change in an external parameter (such as the price of a good) affects the equilibrium outcome of an economic model. It is useful for examining the impact of changes in inputs or market conditions on variables like output and profits.

Supply Function

A supply function represents the relationship between the price of a good and the quantity of that good that suppliers are willing to produce and sell. It is a fundamental concept in microeconomics that helps determine how changes in market prices affect the output levels of firms.

Fixed Costs

Fixed costs are expenses that do not change with the level of output. They are incurred regardless of how much is produced, such as rent or maintenance costs, and play a critical role in profit calculations by contributing to total costs that must be covered by revenue.

Profit Function

The profit function is the relationship that shows how a firm’s profit is determined by the difference between its total revenue and total costs. In this function, total revenue is typically calculated as the product of price and quantity, while total costs include both fixed and variable costs.

Transcript

00:01 Okay, so we're basically going to be looking at this question.

00:04 We are given a supply function, which is equal to 4p.

00:09 And the other piece of information that's given is that a fixed cost are equal to 100.

00:17 And if the price changes from 10 to 20, what is the change in its profits? okay, so we already understand that profit is equal to your revenue.

00:33 Minus costs.

00:35 Okay, so that's the profit.

00:38 So in order for us to really arrive at our solution, the first thing that we'll need to look at is given that function, so what would be the revenues and what would be the cost.

00:54 So let's start off with the revenue.

00:56 We understand that revenue is equal to price times quantity.

01:01 Okay so from from the expression that is given which is q is equal to 4p we can simply substitute the q with a 4p in our in our equation in order to derive the revenue here let me call it r1 because we want to look at when the prices 10 what is the profit okay so we we start off with revenue.

01:34 Okay, so in order to get r1, so we can actually say p times 4p in order for us to be able to derive that the revenue we have.

01:52 Okay, so if the price is 10, so we simply substitute there times four times 10, it would, it would mean, it would mean, that our revenue at the stage is four times 10 gives us 40 times 10 gives us 400 so our revenues are 400 now let's look at our costs i'll use a different for for the when when the price is 10 ten dollars okay so the the costs which i'll just call this c1 here okay should be equal to the we understand that the the cost should be equal to fixed cost plus variable costs okay so in this case we are given with that the firm the firm is in a perfectly competitive market so which means the marginal costs essentially if you just indicated somewhere here the marginal costs are really equal to the price okay competitive market okay so basically you if you are given that the these the marginal cost is 4p so it would simply mean that the the integral of four p uh plus obviously the constant in this case you notice if you enter if you find the integral of p you get two p squared plus a hundred would then summarize our costs so what do we get in this when the price is ten dollars uh plus a hundred you simplify this expression uh ten squared is 100 times 2 is 200 in this case plus a hundred gives you 300 okay so to conclude so to get the profit which i was just say p1 is equal to r1 minus c1 in this case it's basically 400 minus 300 and you get 100 as your answer okay so that is when the price is ten dollars but let's go on with the analysis to check if the price is twenty dollars okay so we using the same approach okay our r2 this time is equal to a price times for p in this case the price is now 20 okay so the 20 times four times 20 should give us the revenue in this case 80 times 20 if you simplify this expression you get 800 dollars okay and the second analysis is on the cost so cost two should be equal to we already have identified that the expression 2p squared plus 100 would give us the total cost there...

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