Group+1+Taxes

= = =Group 1: Taxes=

The supply of beef in the United States is defined by the equation: math P = 5 + 2Q_{S} math while the demand is defined by the equation: math P = 20 - \frac{1}{2}Q_{D} math Please answer the following questions about the U.S. beef market.
 * 1) **Graph the market supply and demand, making sure to label all key points.**

__JIMMY BOWENS__

The supply and demand curve for the above equations is below:




 * 2. What is the equilibrium price and quantity in the beef market.**

__JIMMY BOWENS__

Based on the information provided above, we can solve for the value of the equilibrium price and quantity simultaneously by doing simple algebra.

Before we can do this, however, we must transform the two equations above by solving for the function of quantity demanded and quantity supplied.

math P = 5 + 2Q_{S} math

math Q_{S} = \frac{5}{-2} +\frac{1}{2}P math

and

math P = 20 - \frac{1}{2}Q_{D} math

math Q_{D} = 40 - 2P math

Now we are going to solve for the market equilibrium price and quantity.

math Q_{S} = Q_{D} math

math \frac{5}{-2} + \frac{1}{2}P = 40 - 2P P = \frac{42.5}{2.5} P = 17 math

So the market price is $17, now we are ready to find the market quantity at that price. To do this, we can use either of the previous functions since both the Demand Curve and the Supply Curve meet at the same place. So I am going to use the demand function for this.

math Q_{D} = 40 - 2 (17) math

math Q_{D} = 6 math

So at the market price of **$17** the quantity demanded is **6** pounds of beef.

Hence, the market equilibrium price and quantity in the beef market is: __**6 pounds at the price of $17.**__


 * 3. What is the value of consumer surplus at the current market equilibrium?**

__JIMMY BOWENS__

At the current market equilibrium, the consumer surplus is as follows:

math \frac{1}{2}(6)(3) = 9 math

So consumers are enjoying a surplus of **$9 dollars**, which is the difference between what they are willing to pay and what they actually pay for the beef.

Now assume that the United States has decided to impose a tax of $5.00 on all sales of beef.
 * 1) **Graph the resulting equilibrium. Illustrate on your graph the change in consumer surplus, producer surplus, the tax revenue collected, and the deadweight loss associated with the tax.**

__JIMMY BOWENS__

The effects of a $5.00 tax are demonstrated below:

The new equilibrium quantity of beef sold on the market will be reduced to __about__ **4 lbs.** Because of the tax of $5.00, consumers now have to pay about $18.13 for 4 lbs of beef.
 * 1) **What is the new equilibrium quantity of beef sold on the market.**
 * 1) What price do consumers have to pay for beef? What price do producers earn for their beef?

WESLEY GIFFORD To calculate the elasticity of using the midpoint method, we take the difference between Q 1 and, divide that by the average quantity, and then do the same calculations with P instead of Q. To get elasticity, we divide the results Q by P. For this equation, the elasticity of demand is approximately 7, indicating a very high elasticity.
 * 1) What is the elasticity of demand between the original price of beef and the new price of beef? What about the elasticity of supply?

To calculate price elasticity of supply, we must use the price and quantity of the supply curve not at the new equilibrium, but the price at the new quantity minus the tax. This gives us the price that sellers are actually receiving. Based on this information, the price elasticity of supply is 1.5 - elastic, but considerably less so than the demand curve.
 * 1) How do the elasticity of supply and demand relate to the deadweight loss associated with the tax?

AMER JUNTADO

As prices change, so does elasticity, how consumers and producers respond to changes in prices. Where deadweight loss applies is how an increase in total price could force the consumer to change the product(s) they originally demand for others that seem less affected by the tax burden, hence making a product demanded more elastic due to more choices. However, if a product is inelastic and there is a tax burden, then the deadweight loss is evident as consumers can do little to change to substitutes and must bear the costs of the tax burden.