Skip to main content

Exercise: Price control

Your city council voted to set a price ceiling on the market for good X. The price ceiling is set to be equal to 75% of the current equilibrium price. 

The current market demand can be modeled by the equation:
 
The market supply curve corresponds to the following equation:
 
Using the given information, find:
  • the new price and the new amount of quantity sold 
  • the shortage
  • a tax per unit of good sold that would result in the same quantity that is available at the price ceiling
    • Derive an equation for the new market supply curve with the tax.
First, let's derive the equilibrium price and quantity for this market. Set the demand curve equal to the supply curve.

Now that we know the original price (i.e Pe), we can derive the price ceiling and the quantity sold at that price:
From our notes, we know that the quantity sold at that price must be equal to the amount that can be supplied by the producers. Therefore, all we need to do is to plug the new price into the supply curve equation and solve for Q.

The shortage is the difference between the quantity demanded and the quantity produced at a given price:

So the shortage is equal to 31.25 units. Or in other words, if producers were able to produce 31.25 more units at the given price, no price ceiling would be needed.

In order to find a per unit tax that would result in the same amount of quantity consumed as the price ceiling, one needs to understand that the tax would shift the supply curve to the left. Intersecting the demand curve where the quantity is equal to 12.5 (why?). Once we know the price that consumers are willing to pay, the tax is equal to the distance between the price ceiling and the new price for the demand curve at the given quantity.

Since we found the per unit tax, the new supply curve can be modeled by the following equation:


Let's visualize the problem:



The new supply curve (S2) has the same slope as S1. The only difference is that the constant factor in S2 includes the per unit tax, which causes this leftward shift. Furthermore, the tax is equal to difference between PT and PC on the graph. 









Labels:

Comments

Post a Comment

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 ...
Post a Comment
Read more

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 ...
Post a Comment
Read more

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...
Post a Comment
Read more