Question

Saxum Vineyard, in Paso Robles, CA, is one of the more than 8,000 wineries in the United States. While Saxum produces a number of different kinds of wine, they focus their production on Syrah (also known as Shiraz). Saxum sells their wines all over the United States. Suppose you manage a vineyard like Saxum and want to determine how much you should charge for your Syrah. Suppose the market demand function for Syrah is as follows.

QD = 200 - 38.18PO + 8.35PS - 2Pc + 10Inc + .8TS + .5M21

Where QD is monthly demand for bottle of Syrah (in millions), PO is the price of Syrah in the market, PS is the average price of substitute bottles of wine (other varieties), Pc is the average price of a pound of cheese and is used to gauge the price of complimentary goods, Inc is average US per capita income (in thousands), TS is the number of wine trade shows and competitions each year which firms can attend to market their wines, and M21 is the number (in millions) of millennials in the US over the age of 21. This last variable is included to capture a change in consumer preferences; millennials are drinking wine at a much higher rate than previous generations.

The market for Syrah also has supply, produced by wineries similar to Saxum Vineyard and your winery, which can be stated as follows.

QS = -100 + 22.93PO - 5PPI - 10PS + 8Temp + 1Sup

Where QS is monthly supply of bottles of Syrah (in millions), PO is the price of Syrah in the market, PPI is the Producer Price Index (an index used to gauge changes in the costs of production in the US), PS is the price of substitute wines which could easily be produced instead of Syrah, Temp is the expected temperature during the harvest season for grapes, and Sup is the number of wineries that supply Syrah in the market (in thousands).

Using the market supply and demand functions for Syrah given, fill in the template provided with the coefficients for each function.

Using the information below, fill in the values for each of the variables except Price of Syrah.

Demand:

-Price of Substitutes: $18

-Price of Cheese: $15

-Income: $53,000

-Trade Shows/Competitions: 3

-Millennials = 45 million

Supply

-PPI: 111

-Price of Substitutes: $18

-Temperature: 60

-Number of Suppliers: 8,000

a)   When the price of Syrah increases by $1, do supply and demand increase or decrease?                                  
b)   By how much? What is the effect on quantity demanded and quantity supplied?                                   
                       a)       b)      
                   Quantity demanded ____ by _______ million bottles.  
                   Quantity supplied ________ by _________ million bottles.  
c)   Does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves to the left or right?
                                  
d)   By how much?

                                  
                       c)       d)      
                   Demand curve is shifted to the _______ by ________ million bottles.  
                   Supply curve is shifted to the ________ by __________ million bottles.  
e)   Suppose the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly?

                                  
                   Price of Syrah =   $22.00              
                   Bottles demanded = _______ million          
                   Bottles supplied = _________ million          
f)   Is there a shortage or a surplus?

  
g)   How much is the shortage or surplus?

                                  
                       f)       g)      
                   There is a _______ equal to _______ million bottles.  
h)   If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly?

                                  
                   Price of Syrah =   $16.00              
                   Bottles demanded = __________ million          
                   Bottles supplied = ________ million          
i)   Is there a shortage or a surplus?

                                  
j)   How much is the shortage or surplus?                                  
                       i)       j)      
                   There is a ________ equal to _______ million bottles.  

                                  

Answer 1

Demand function

QD = 200 - 38.18PO + 8.35PS - 2Pc + 10Inc + .8TS + .5M21

Given

-Price of Substitutes: $18

-Price of Cheese: $15

-Income: $53,000

-Trade Shows/Competitions: 3

-Millennials = 45 million

So,

QD = 200-38.18PO+ 8.35PS-2Pc+10Inc+0.8TS +0.5M21

QD = 200-38.18PO+ 8.35*18-2*15+10*53+0.8*5+0.5*45

QD=875.20-38.18PO

Supply function

QS = -100+22.93PO-5PPI-10PS+8Temp+1Sup

Supply

-PPI: 111

-Price of Substitutes: $18

-Temperature: 60

-Number of Suppliers: 8,000

QS =-100+22.93PO-5*111-10*18+8*60+1*8

QS=-347+22.93PO

a)

When the price of Syrah increases by $1, do supply and demand increase or decrease?                      

Slope of PO in demand equation=-38.18

Slope of PO in demand equation is negative. It means that quantity demanded will decrease in response to $1 increase in Syrah prices.

Slope of PO in supply equation=22.93

Slope of PO in supply equation is positive. It means that quantity supplied will increase in response to $1 increase in Syrah prices.

b)   By how much? What is the effect on quantity demanded and quantity supplied?                               
Slope of PO in demand equation=-38.18

It means the quantity demanded will decrease by 38.18 million for every $1 increase in price if Syrah.

Slope of PO in supply equation=22.93

It means the quantity supplied will increase by 22.93 million for every $1 increase in price if Syrah.

c)   Does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves to the left or right?
                                  
Slope of PS in demand equation=+8.35

Slope of PS in demand curve is positive. It means that demand will increase in response to $1 increase in substitute. Demand curve will shift to right.

Slope of PS in supply equation=-10.00

Slope of PS in supply curve is negative. It means that supply will decrease in response to $1 increase in substitute. Supply curve shifts to left.

d)   By how much?

Shift in demand/supply curve will be equal to slope of demand/supply curve following a $1 increase in price of substitute.

Demand curve is shifted to the right by 8.35 million bottles.  
Supply curve is shifted to the left by 10.00 million bottles.  

e)   Suppose the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly?

QD=875.20-38.18PO

QD=875.20-38.18*22 =35.24 million

QS=-347+22.93PO

QS=-347+22.93*22=157.46

Price of Syrah =   $22.00              
Bottles demanded = _35.24_ million          
Bottles supplied = 157.46_ million          

f)   Is there a shortage or a surplus?

Supplied quantity is larger than quantity demanded, there is a surplus in the market

  g)   How much is the shortage or surplus?

Surplus=157.46-35.24=122.22

h)   If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly?

QD=875.20-38.18PO

QD=875.20-38.18*16 =264.32 million

QS=-347+22.93PO

QS=-347+22.93*16=19.88

Price of Syrah =   $16.00              
Bottles demanded = _264.32_ million          
Bottles supplied = 19.88_ million          

i)   Is there a shortage or a surplus?

Quantity demanded is larger than quantity supplied. There is a shortage in the market.                                 

j)   How much is the shortage or surplus?                                  
Shortage=264.32-19.88=244.44 million