Evaluate the estimated demand model. - Economics questions

Demand elasticity is used to measure the sensitivity of consumer demand for a product or service based on changes to variables such as price and income. Applying our data for Demand of Pork, Price of Pork, Price of Beef and Income we can calculate these elasticities of demand. In the sections below we will calculate and interpret the price elasticity of demand, income elasticity of demand and the cross-price elasticity of demand.

Our extended demand equation is QD=63.63-13.01Pp+1.95Pb+.24M, where Pp is the price of pork, Pb is the price of beef and M is income. Using the data from 2015 we can create a reduced demand equation to estimate the quantity of pork.

QD = 63.63 -13.01Pp + 1.95 (4.38) + .24 (67)

Reduced demand equation = QD = 88.25 – 13.01Pp

When the Price of pork = 3.11, then QD = 47.79

We can now use the elasticity of demand calculation to determine the effect on demand if we increase the price of pork by $1. If we input a $1 increase of price, 4.11, into the reduced demand equation we calculate an estimated quantity demanded of 34.78. Now we can solve for the price elasticity to observe the effects of this increase.

Price Elasticity of Demand = ( in QD Pork/ in P Pork)*(P Pork Avg/ QD Pork Avg)

E = ((34.78-47.79)/(4.11-3.11))*((4.11+3.11)/2)/(34.78+47.79)/2)) = -1.14

How do we interpret -1.14? With an elasticity greater than 1 the demand for this product is elastic. Elastic goods and services tend to have more substitutes available. As the price increases the demand can drop dramatically because consumers can purchase alternative products to replace it. From our calculations for Pork we find that if the price of pork increases 10% you will see an 11.4% decrease in quantity of pork demanded, on the other hand if there is a 10% decrease in the price of pork there will be a 11.4% increase in its demand. Based on our assumptions you can see below that raising the price of pork by $1 will decrease revenues.

Total Pork revenue with Price of Pork at $3.11 = Q * P = 47.79 * 3.11 = 148.63

Total Pork revenue with Price of Pork at $4.11 = Q * P = 34.78 * 4.11 = 142.95

Next we will focus on the Income elasticity. Income is a significant variable when analyzing elasticities. Changes in income levels ultimately change the quantities demanded of goods all other factors remaining the same. Using the same 2015 data we can create a new reduced demand equation to calculate elasticity based on a change in income.

QD = 63.63 -13.01 (3.11) + 1.95 (4.38) + .24M

Reduced demand equation = QD = 31.71 + .24M

When the Income is = 67, then QD = 47.79

We can now use the elasticity of demand calculation to determine the effect on demand if we increase the income by 10. If we increase income to 77 and input this into the reduced demand equation, we calculate an estimated quantity demanded of 50.19. Now we can solve for income elasticity and observe the effects of this increase.

Income Elasticity of Demand = ( in QD Pork/ in Income)*(Income Avg/QD Pork Avg)

E = ((50.19-47.79)/(77-67))*((77+67)/2)/(50.19+47.79)/2)) = .35

With an elasticity greater than 0, the interpretation of .35 elasticity is that this good is a normal good. The fact that the elasticity is less than 1 also indicates that this good is a necessity. All other elements held constant a 10% increase in income will result in quantity demanded increasing by 3.5%. Displayed below is the affect that this change would have on revenues.

Total Pork revenue with income at 67 = Q * P = 47.79 * 3.11 = 148.63

Total Pork revenue with income at 77 = Q * P = 50.19 * 3.11 = 156.09

Our final elasticity that we will calculate and interpret is the cross-price elasticity of demand. This concept is used to measure the responsiveness of quantity demanded of good X, in our case pork, to the change in price of a related good Y, in our case beef.

QD = 63.63 -13.01 (3.11) + 1.95Pb + .24(67)

Reduced demand equation = QD = 39.25 + 1.95Pb

When the Price of Beef is = 4.38, then QD = 47.79

Again using the 2015 data we calculate the quantity demanded for pork. While holding all other factors constant, an increase in the price of beef by $1, we can calculate a new estimated quantity demanded of 49.74. Using these figures, we can determine the cross-price elasticity of demand.

Cross-Price Elasticity of Demand = ( in QD pork/ in Pb)*(P Beef Avg/ QD Pork Avg)

E = ((49.74-47.79)/(5.38-4.38))*((5.38+4.38)/2)/(49.74+47.79)/2)) = .195

A cross-price elasticity greater than 0 indicates that these are substitute goods. If the price of good Y increases 10% the quantity demanded of good X will increase 1.95%. Below we show the revenue impact for pork when the price of beef increases by $1.

Total Pork revenue with Price of Beef at $4.38 = Q * P = 47.79 * 3.11 = 148.63

Total Pork revenue with Price of Beef at $5.38 = Q * P = 49.74 * 3.11 = 154.69