Skip to main content

Exercise: Price elasticity

If you know that the market demand for good X corresponds to the following equation:
and the supply curve can be model by the equation:
Calculate the price elasticity for each curve at the equilibrium point. Furthermore explain which curve is relatively more elastic.

The first step consists of solving for the equilibrium price and quantity:

Remember the formula for the price elasticity is


Therefore pick the two closest points and calculate the price elasticity, in this case let's pick a point that is one quantity less than the equilibrium point on both curves.


Since we are dealing with linear equations we can use another formula which is specific for these types of curves and is more precise than the method we used so far. The formula is the fraction of the price over the quantity multiplied by the inverse of the slope.


Since Ed>Es, the demand curve at the equilibrium point is relatively more elastic than the supply curve. Note that both curves are elastic since both have an elasticity greater than 1. Furthermore, one could have made an educated guess by just looking at the absolute value of the slope for each curve. 


The State wants to impose a price floor on the market for good X where the price elasticity of demand is equal to 6. Derive the equation for the price floor.

To answer this question, let's remember that one way to derive the elasticity for a linear function is by using a formula that combines the price, quantity and slope of a linear curve. Therefore, if we know the elasticity, we can create a linear function that intersects the demand curve at the price floor. 


Thus, since the equation of a price floor is only bounded by the price, its equation is equal to P=385.6, at this point the price elasticity of the demand curve is about 6.
Let's visualize the problem:



Labels:

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: equilibrium in the AD/AS model

Real output and price level in the AD/AS model: The short run equilibrium in the AD/AS model, is when the  intersection between the short run aggregate supply curve and the aggregate demand curve determines the level of output and price level.          This short equilibrium output can be compared to the full-employment (i.e long run equilibrium) output by adding the long run aggregate supply curve in the graph.  If the difference between the short run equilibrium output and full employment output is negative than we have a recessionary gap. This could be caused by a decrease in households' consumption, a fall in private investments, or a decrease in government spending. If the difference is positive, we have an inflationary gap, where the short run equilibrium output is bigger than its full employment output. This can be caused by an increase in households expenditures, expansionary fiscal policy, etc... If the gap is zero, this means that t...
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: 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