SUPPLY AND DEMAND At 0.60 per bushel, the daily supply for...

SUPPLY AND DEMAND At $\$ 0.60$ per bushel, the daily supply for wheat is 450 bushels and the daily demand is 645 bushels. When the price is raised to $\$ 0.90$ per bushel, the daily supply increases to 750 bushels and the daily demand decreases to 495 bushels. Assume that the supply and demand equations are linear. (A) Find the supply equation. (B) Find the demand equation. (C) Find the equilibrium price and quantity.

SUPPLY AND DEMAND At $\$ 0.60$ per bushel, the daily supply for wheat is 450 bushels and the daily demand is 645 bushels. When the price is raised to $\$ 0.90$ per bushel, the daily supply increases to 750 bushels and the daily demand decreases to 495 bushels. Assume that the supply and demand equations are linear.
(A) Find the supply equation.
(B) Find the demand equation.
(C) Find the equilibrium price and quantity.

Key Concepts

Linear Models in Economics

Linear models simplify complex economic relationships by assuming a straight-line relationship between variables, such as price and quantity. In the context of supply and demand, linear equations are often used to model how changes in price affect the quantities supplied and demanded, making analysis and prediction more straightforward.

Market Equilibrium

Market equilibrium occurs at the point where the supply curve intersects the demand curve, meaning the quantity supplied equals the quantity demanded at a particular price. This concept is pivotal in economics as it represents a state where there is no inherent force causing the market to change, barring any external influences.

Systems of Linear Equations

A system of linear equations involves two or more linear equations that are solved together because they share common variables. In economic problems, such as finding the equilibrium in a market, solving a system of equations is critical to determine the price and quantity that satisfy both the supply and demand relationships simultaneously.

Supply Curve

A supply curve represents the relationship between the price of a good and the quantity that producers are willing to supply. Typically, it is upward sloping, indicating that higher prices incentivize producers to supply more of the good, and is a fundamental concept in understanding market behavior from the producer’s perspective.

Demand Curve

A demand curve describes the relationship between the price of a good and the quantity that consumers are willing to purchase. It is generally downward sloping, reflecting the idea that consumers tend to buy less of a good as its price increases, and it's essential in analyzing consumer behavior in a market.

Transcript

00:03 Here we have the price and quantity comparisons of supply and demand for bushels of wheat.

00:11 So we can see as this price increases from 60 cents to 90 cents per bushel, the supply quantity increases, but in that same price increase, the demand decreases.

00:25 So we want to come up with our supply equation and our demand equation to our ultimately find that equilibrium point where supply equals demand.

00:36 So how we want to go about doing this is finding your rate of change, thinking about rate of change being slope, which is your change in y over your change in x.

00:48 In this case, we're going to say change in p over change in q.

00:56 We're going to do that for both supply and demand.

00:59 So remember change in your p, is essentially that formula y2 minus y1 over x2 minus x1 so that gives us 0 .3 over 300 which simplifies to 0 .001 and again that's essentially the slope and we're thinking in terms of y equals m x plus b we have different letters here so we're going to say p equals 0 .001 1q and then we likely have some unknown kind of y intercept value there.

01:46 So what we do define that y intercept is to substitute values of p and q into our equation so we could say 0 .6 and 450 for p and q respectively.

02:04 Equals 0 .001, q is 450 plus b.

02:13 Solve this and we get b equals 0 .15, which makes our equation for supply as p equals 0 .01q plus 0 .15.

02:35 Now let's try to do the same thing with demand.

02:40 That same rate of change in our p value of 0 .3 but now our quantity decreased by negative 150 and that simplified to negative 0 .002 so go ahead and kind of make my equation like we did before so p equals 0 .002 so negative q plus some unknown value, i can replace pieces from my table into p and q.

03:23 So i could say 0 .6 equals negative .002 times 645.

03:35 And solve this for b and i get b equals 1 .89.

03:43 And then just plug that back into that demand equation...

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