Question

In: Economics

PX = $9500 PY = $10000 I = $15000 A = $170000 W =...

PX = $9500 PY = $10000 I = $15000 A = $170000 W = 160
This function is:
Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W

1. Use the above to calculate the arc price elasticity of demand between PS = $8000 and PS = $7000. The arc elasticity formula is:
Ep= Q/P8 * P1+P1/Q1+Q2

2. Calculate the quantity demanded at each of the above prices and revenue that will result if the quantity is sold (fill in table below).
PS     QS   Revenue
$8000
$7000

3. Marketing suggests lowering the price PS from $8000 to $7000. The size of the elasticity coefficient in #1 should tell you what is likely to happen to revenue. Explain why this is (or is not) a good marketing suggestion from a revenue viewpoint (note: your answer in #1 and the calculations in #2 should be giving the same message). If the implications in #1 and #2 differ, does the difference make sense (or did you make a mistake in #1 or #2)?

4. Calculate the point price elasticity of demand for Smooth Sailing boats at PS = $8000 (which should make QS = 141600). Does this elasticity value indicate that demand for Smooth Sailing boats is relatively elastic? Explain why or why not. The formula is:
Qs/Px *Ps/Qs

5. Calculate the point cross-price elasticity of demand between Qs and Px with Px = $9500. Use Qs corresponding to Ps = 8000. Other variables and their values are as given at the top, before question #1. Does this elasticity indicate that the demand for Smooth Sailing’s boats is relatively responsive to changes in Px? Explain why or why not. The formula is:

Esx= QS/Px*Px/Qs

6. Calculate the point cross-price elasticity of demand between QS and Py, given that Py = 10000 and that PS = $7500 (thus QS should equal 161,600). Other variables are as given at the top before #1. Does this elasticity indicate that the demand for Smooth Sailing boats is relatively responsive to changes in Py? Explain why or why not. The formula is:
Esy= Qs/Py *Py/Qs

Solutions

Expert Solution

Given,

Plug in all the given values

When Ps = $ 8,000

When Ps = $ 7,000

1. Elasticity can be measured as

Elasticity of demand = - 1.8564

2. When Price = $ 8000, Qs = 141,600

TR = 8,000 × 141,600 = $ 1,132,800,000

When Price = $ 7000, Qs = 181,600

TR = 181,600 × 7000 = $ 1,271,200,000

3. The elasticity of demand is 1.85 that is elastic therefore, the firm can increase their total revenue if they will reduce the price of the product.

On the same line we can see the Total revenue of the firm has increased it's revenue by reducing the price from $ 8,000 to $ 7,000.

4. Calculating the point elasticity

The price elasticity of demand is elastic. Since, the elasticity of demand is greater than 1.

5. The point cross elasticity can be measured as

The cross elasticity is positive. Therefore the two good are substitute to each other.

6. Cross elasticity between S and Y

The two good are substitute.

If any query kindly contact through comments. Will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.

Rahul Sunny answered 2 weeks ago

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