A The price elasticity of demand for imported whiskey is es

A - The price elasticity of demand for imported whiskey is estimated to be ?0.20 over a wide interval of prices. The federal government decides to raise the import tariff on foreign whiskey, causing its price to rise by 30 percent.

1 - Will the quantity demanded on imported whiskey rise or fall, and by what percentage amount?

2 - What is the percentage change in the total revenue after the tariff increases?  

B - The XYZ Company developed the following quarterly sales forecasting model:

Y_t = 6.32 + 0.01t   

where Y_t = predicted sales ($ million) in quarter t; t = 1 (First quarter of 2008), 2 (Second quarter of 2008), 3 (Third quarter of 2008), and so on.

3 - Given the time-series model, what is the period t for the fourth quarter of 2018?

4 - How much is the predicted sales for the fourth quarter of 2018?

Solution

Solution: Price elasticity of demand, ed = -0.20

A. 1) Since, ed is negative, this means there exists inverse relation between price and quantity demanded. So, the 30% increase in price will cause quantity demanded to fall.

ed = percentage change in quantitydemanded/percentage change in price

-0.2 = percentage change in quantity demanded/30

Thus, percentage change in qty demanded = -0.2*30 = -6. So, qty demanded will fall by 6%.

2)Total revenue = price*quantity. Say initially price, P= $y, and qty demanded, Q =x unit

After price change, P\' = y(1 + 0.3) = 1.3y

and, Q\' = x(1 - 0.06) = 0.94x

So, TR = xy and TR\' = (1.3y)*(0.94x) = 1.222xy

TR\' = (1 + 0.222)xy = (1+0.222)TR (Extra Note: Since, 1.222 > 1, there has been an increase in the total revenue)

So, percentage change in total revenue = 22.2%

B. 3) First quarter of 2008 implies t = 1

We have to find value of t, for fourth quarter of 2018.

Given the time-series, every fourth quarter of an year gives value of \'t\' as a multiple of 4.

Then, fourth quarter of 2008 gives t = 4

fourth quarter of 2009 gives t = 8 (=4*2) and so on.

Following this pattern, we get an arithmetic progression series: 4, 8, 12, ....

If 1st term is for 2008, 2nd for 2009, 3rd for 2010, and so on, then what term is for year 2018? Say it is \'n\'

So, n = (2018 - (2008 + 1)) = 11

We have to find 11th term of the series 4, 8, 12....., Here first term = a =4, common difference = d =8-4 = 4

Formula for nth term = a + (n - 1)*d

So, 11th term = 4 + (11 - 1)*4 = 44. So t = 44

4) Yt = 6.32 + 0.01t

For t = 44, Yt = 6.32 + 0.01*44 = 6.76

So, predicted sales for the fourth quarter of 2018 = $6.76 million.