Skip to main content

Exercise: How to Measure Welfare

You are tasked by your city council to find the economic surplus the market for good X creates. Furthermore, the council members want to know how the economic value is divided between the producers and the consumers. Lastly, calculate the tax burden for each party ,the dead weight loss, and the revenue that would go to the city's budget if a per unit tax of $15 is imposed on the producers.

You know that the demand schedule is,
and the supply curve can be modeled by the following equation;

In order to find the consumer and producer surpluses, one need to first solve for the equilibrium price and quantity:

Now that we know the equilibrium price and quantity we can find the consumer surplus and the producer surplus. In this problem I will demonstrate two ways to solve this exercise. The first method uses algebra, which is well suited for this type of question, since the demand and supply curves are linear. The second method is more general and involves the use of Calculus.
  • 1st method:

Notice that both areas are triangles. Therefore, we can use the formula for the area of a triangle to find both surpluses.

The total economic surplus is equal to $902.5.
  • 2nd method:
Since we know that for the consumer surplus, the area is bounded by demand curve from above and by the equilibrium price from below. We can set up a double integral to find the area:

The same idea can be applied for the producer surplus, the area is bounded above by the equilibrium price and by the supply curve from below;
If the city introduces a per unit tax of $15 on good X, then supply curve shifts to the left and is now equal to:
 
Solving for the equilibrium price and quantity we see that the market clearing price is $103 and 16 units are sold at that price.

The tax incidence on the producers and consumers is calculated by looking at the ratio of the change in price to the per unit tax.
One nice way to check if you have the correct answer is if the sum of the tax burden for both parties add up to 1. Furthermore, we see that 40% of the tax is 'payed' by the consumers while the suppliers take on most of the tax (60%).

 To calculate the dead-weight loss, realize that this area is a triangle. We can use the same formula utilized to find the consumer and producer surpluses.

This means that the new total economic surplus is equal to $880 after the tax.

The revenue that will go the city's budget  corresponds to the number of units produced times the tax.


let's visualize the problem:

Labels:

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: real vs nominal gross domestic product

Nominal GDP:   A nominal GDP measures the value of a nation's output produced in a year, given the prices charged for that year. However, if prices increase while the output level stays constant in a given year, the nominal GDP will drastically increase, even though the level of production is equal to that of the previous year. Estimating real GDP: To determine the actual change in output from one year to the next, we must adjust the nominal value of a country's output in a year based on changes in the average price level during that year.  Inflation is when the price level increases, whereas deflation is when the price level is decreasing. To determine whether the nominal GDP overestimates or underestimates the output of a country, one must know whether the average price level has increased or decreased. In order to achieve this task can use a price index known as the GDP deflator. The GDP deflator: Real GDP is calculated by replacing the prices for that current year with tho...
Post a Comment
Read more

Microeconomics: Firms and cost in the short run

In Economics, the term short run refers to a time period where at least one variable of interest does not change . In our case, the short run for a firm is when at least one input  (labor, land, capital) stays fixed. Usually land and capital are considered fixed in the short run.  If an input is fixed during a period time, no matter how much the total product a firm produces, its cost stays the same. This cost is commonly known as fixed cost (FC). Examples of fixed costs: rent, property taxes, loan payments. Labor is often considered to be a part of the  variable cost (VC) . Variable cost can be defined as the cost a firm has control over during the short run. Unlike fixed cost, variable cost increases (decreases) as a firm's total product increases (decreases). Examples of variable costs include: utility bills, wages, raw materials A firm's total cost (TC) is the sum of its variable and fixed costs. As you can see, the fixed cost...
Post a Comment
Read more

Macroeconomics: the money market and loanable funds market

  The money market: The money market combines the supply of money and the demand for money for a country. The supply curve (Sm) is inelastic and is determined by the central bank. The demand curve (Dm) is the horizontal summation of the asset and transaction demand curves and is sloping downward. The intersection between the Sm and Dm is the equilibrium interest rate for a country. A change in the nominal interest rate implies that either or both curves (i.e Sm and Dm) have shifted to the right or left. An increase in nominal GDP (P*Y) will lead to an increase in the transaction demand for money which will shift the total demand (Dm) to the right. The nominal interest rate goes up. A decrease in the level of output (Y) will shift the Dm curve to the left. The Sm curve will shift whenever the central bank decides to change the money supply due to a monetary policy decision. The Fed expands the supply of excess reserves in commercial banks, by purchasing bonds from banks, Sm shi...
Post a Comment
Read more