The demand curve for a product is given by q= 120,000-500 p...

The demand curve for a product is given by $q=$ $120,000-500 p$ and the supply curve is given by $q=$ $1000 p$ for $0 \leq q \leq 120,000,$ where price is in dollars. (a) At a price of $\$ 100,$ what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push prices up or down? (b) Find the equilibrium price and quantity. Does your answer to part (a) support the observation that market forces tend to push prices closer to the equilibrium price?

The demand curve for a product is given by $q=$ $120,000-500 p$ and the supply curve is given by $q=$ $1000 p$ for $0 \leq q \leq 120,000,$ where price is in dollars.
(a) At a price of $\$ 100,$ what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push prices up or down?
(b) Find the equilibrium price and quantity. Does your answer to part (a) support the observation that market forces tend to push prices closer to the equilibrium price?

Key Concepts

Demand Curve

A demand curve represents the relationship between the price of a product and the quantity that consumers are willing to purchase at each price level. It typically slopes downward because higher prices reduce the quantity demanded, highlighting consumer behavior and the law of demand.

Supply Curve

A supply curve illustrates the relationship between the market price and the quantity that producers are willing and able to offer for sale. It usually slopes upward, reflecting that higher prices incentivize producers to supply more, in line with the law of supply.

Market Equilibrium

Market equilibrium occurs at the point where the quantity demanded by consumers equals the quantity supplied by producers. At this balance, there is no inherent pressure for the price to change, as the plans of buyers and sellers are perfectly matched.

Excess Demand and Excess Supply

Excess demand exists when the quantity demanded exceeds the quantity supplied, creating upward pressure on prices as consumers compete for the limited supply. Conversely, excess supply happens when the quantity supplied surpasses the quantity demanded, which typically drives prices down as producers attempt to sell surplus inventory.

Price Adjustment Mechanism

The price adjustment mechanism is the process through which market prices change in response to surpluses or shortages. When there is excess demand, prices tend to rise; when there is excess supply, prices tend to fall. This mechanism drives the market toward the equilibrium point over time.

Transcript

00:02 Hello, in this problem we're given the demand and supply curves by way of their equations.

00:11 The demand curve is given with this equation, the supply curve is given with that.

00:17 And we want to know when the price is $100, when the price is $100, what quantities are consumers willing to buy, willing to buy? the quantity that consumers are willing to buy.

00:46 We look to the demand.

00:49 This is the demand function.

00:54 The demand function tells us what quantity consumers are willing to buy when a price is a given price.

01:02 And they also want to know the quantity.

01:05 The producers are willing to supply.

01:08 So the quantity, let's call this q1 and q2.

01:12 The quantity that the producers are willing to supply.

01:26 Okay, at this point it might not be a bad idea to graph these two functions on the same coordinate axis.

01:36 Keeping in mind that we place q on the horizontal axis and p is here.

01:43 So we will be graphing functions like this is where are usually our x's.

01:51 And y axis then so we will plot functions as x equals a function of y.

02:00 Let me show you what i mean.

02:04 Okay, i just popped into this month .com.

02:10 And q, which is on the x -axis, is equal 120 ,000 minus 500 p, which is on the y -axis.

02:18 And this would be our demand curve and this would be our supply.

02:32 Alright? we can approximate the equilibrium point to be at 80 ,000 units at which the price will be here and if we read this as 60 70 80 so this would be at 80 dollars.

03:00 P is in dollars.

03:03 All right, just to give us a rough idea what we expect.

03:07 Now, in this question a, when the price is 100, when the price is 100, p, the price is 100, we look what the demand is for 100 and we look what the supply is for 100, which will be around here.

03:30 And from the graph we can tell that the supply is greater than demand when the price is 100.

03:40 And when supply is greater than the demand, the prices will go down.

03:49 Prices go down when supply is greater than the demand.

03:59 When the demand is higher than the supply, then because of the competing customers, the actual products sell at a greater price.

04:11 So, in advance, we answer the question the second question will the market push prices up or down the prices will go down towards this equilibrium price of 80 but we need to calculate all this so let's calculate what the demand is what q what the demand let's call them demand and supply rather than 1 and 2 the quantity of demand is 120 ,000 minus 500 times 100.

04:49 We substituted p equals $100 into this equation here...

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