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: 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

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

Macroeconomics: foreign exchange market

A currency exchange rate tells us about the value of a currency relative to another currency.  We say that a currency appreciates when its relative value goes up. We say that a currency depreciates when its relative value decreases. In a market that relates two currencies, if one appreciates, it must be the case that the other currency depreciates.  Demand in the foreign exchange market: it represents the quantity of a currency demanded by agents who are holding other currencies. The agents want to buy goods, services, or financial assets from a country whose currency is demanded. The demand must be downward slopping. The weaker the currency, the more attractive the goods produced in that country are, and foreign consumers need to hold more of that currency in order to buy the products. Thus, a change in the exchange rate leads to a movement along the demand curve. Supply in the foreign exchange market: it represents the willingness of people in the country supply to foreigner...
Post a Comment
Read more