Skip to main content

Finding the market equilibrium price and quantity

Finding the equilibrium price and quantity is perhaps one of the most common problems in an introduction to Microeconomics course, which is exactly what we are going to do in this post!

Consider the following problem, you are tasked with finding the equilibrium price and quantity for a particular good X. 

You are told that the producers are willing and able to sell 2 units for the  price of 16 U.S dollars a unit, and if the price increases, they are able to make 10 units for a price of 20 U.S dollars per unit. Assuming that the supply curve is linear, then it can be modeled by the following equation:

 
The same process can be used to determine the market demand (assuming linearity and that we are given information about the market demand schedule). At a price of 30 U.S dollars consumers are willing to buy 10 units, if the price decreases to 12 U.S dollars, consumers want to buy 20 units. Thus the demand curve corresponds to this equation:

Finally, all we need to do is to set both equations equal to one another and solve for P. Remember, the equilibrium price and quantity are determined by the intersection of the demand and supply curves (note that in the equation below P=Pe).


Now that we have the equilibrium price, we can plug this result in any of our two previous equations representing the market demand and supply curves and solve for Q. They should both  give the quantity demanded when the market is in equilibrium. This is also a nice way to double check your work (i.e if you get two totally different results you probably made a mistake somewhere).

 
Let's visualize that:



In a more realistic fashion, we would say that the market clearing price is 20.91 U.S dollars and the quantity of goods provided is 12 units. It would not make much sense to buy 11 units plus 82% of one good, so we can round that number to 12.

Source: example inspired from Zeder,Raphael.How to Calculate the Equilibrium Price. Quickonomics (2018). 

Comments

Popular posts from this blog

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever   any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP).  Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...

Exercise: maximizing profit

Assume that you are the owner of a small business that produces T-shirts. Your the total revenue for your business can be modeled by the following equation: and your total cost corresponds to this function: Find the point at which your firm maximizes its profit. Then, find how much profit the firm if able to earn at that point. Using the total cost and total revenue functions we can set up the profit function: Then, realize that if you want to find the maximum profit, take the derivative of the function and set it up equal to zero, and solve for Q. This is equivalent of taking the derivative of the total cost and total revenue functions and setting them equal to each other. In this problem, I chose the latter option as it was explained in the previous lessons. Notice that profit is often denoted by a capital pi.  We are assuming that the TR>TC for some positive value, you can check for yourself. However, if we did not know that, we would first take the first ...

A short interlude...

Hello all, it's been quite some time since I have made any major announcements since the creation of this blog about a year and a half ago. I am currently in graduate school and will soon take a portion of my comprehensive examination (i.e exams in Micro, Macro, and Metrics that will allow me to continue my studies in my graduate program), wish me luck! Thus, I will not be able to post consistently until at least mid-June. The roadmap is as such, if I pass, I will start introductory lessons in Econometrics and Statistics (if not, then I'll have to study until I can retake the comps in August). I hope that once I am done, I will be able to add more advance materials to the blog, such as general equilibrium, indirect utility functions, and game theory/mechanism design for Micro. The Solow, Ramsey, RBC, New Keynesian models, permanent income hypothesis (PIH) and more for Macro. By the way I think I still need to add notes on the IS-LM curves, so I will do that before jumping to t...