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: 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: inflation and GDP deflator

You have the following table containing information about country Y's GDP deflator, nominal, and real GDP. If the base year is 2015, fill in the blanks and then find the annual inflation rate for each year. Year  Nominal GDP  GDP Deflator  Real GDP 2015 $23,457 100 $23,457 2016 $25,752 ... $23,943 2017 $25,982 108.1 ... 2018 $26,016 ... $25,431.1 2019 $26,323 105.5 ... Solution: Year  Nominal GDP  GDP Deflator  Real GDP   Inflation rate 2015 $23,457 100 $23,457 n.a 2016 $25,752 107.6 $23,943 7.6% 2017 $25,982 108.1 $24,035.2 0.45% 2018 $26,016 102.3 $25,431.1 -5.37% 2019 $26,323 105.5 $24,950.6 3.13%  GDP deflator for the year 2018: Real GDP for the year 2017: General formula to find real GDP by re-arranging the GDP deflator formula: Notice that the sub-index i is for the year. The (annual) inflation rate is simply the growth rate of prices from a year to its previous year: Inflation rate of the year 2018: Notice that in 2018 country Y experienced...
Post a Comment
Read more

Microeconomics: Factor Markets

Definition: Factor markets: markets for the factors of production (example: labor and capital). Markets are formed whenever consumers and producers meet to exchange goods or services. Deriving factor demand: the demand for goods or services in the product markets creates demand for the factors of production.  An increase (decrease) in demand for good X leads the suppliers to increase their production thereby increasing (decreasing) the demand for the factors of production.   Marginal revenue product: The demand for the factor of production is formed by multiplying a firm's marginal revenue by its marginal product.  Remember that by taking the derivative of the TR function with respect to Q we are able to find the MR. Marginal product on the other hand is found by taking the derivative of the production function with respect to a factor of production (L or K for example). Marginal revenue product (MRP): the change in total revenue when one more input is employed. It decrea...
Post a Comment
Read more