The Demand Function for Product X is Given By

8/13/2019 The Demand Function for Product X is Given By

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The demand function for Product X is given by:

= 800- 2Px- 0.05Px -0.2Py + 4Pz + 0.01I+ 2A

Where

Px Price of good

X

$120.00

Py Price of

related good y

$100.00

Pz Price of

related good z

$40.00

I Income $7000.00

A Advertising $250.00

a. (i) Calculate the own Price elasticity of demand (PED) for Good X.

-2(120)-0.05(14400)-0.2(100)+4(40)+0.01(7000)+2(250)

=550

The quantity demanded is equal to 550 which was found using the demand function above.

Now the function must be differentiated to find out how much quantity demanded would change with

respect to the price of good X:

Q/P * P/Q

Letsfind Q/P

Q= 800- 2P-0.05

Q/P= -20.1 P

If P = 120 then,


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(iii) Illustrate on a well labelled demand graph for Product X, the Total Revenue earned when

Price is equal to $120.00.

Using the formula for total revenue= Price * Quantity

Where Price = $120, and Quantity demanded as found in a(1) = 550

From the graph below it is seen that price=$120 and quantity demanded =550 therefore total

revenue earned;

Total revenue is therefore equal to 120* 550 = $66000

Demand Graph Showing Quantity plotted Against Price

Price Price Elasticity of Demand = -3.05

Point; P= $120, Q=550

550 Quantity

b. (i) Determine the Cross-Price elasticity of demand (XED) between Good X and Good Y.

Cross Price Elasticity of Demand = % change in quantity demanded for one good/ % change in

price of a related good

120


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; Good Y increased from $100 to $140

Therefore the new demand function will read

-2(120)-0.05(14400)-0.2(140)+4(40)+0.01(7000)+2(250)

Using the Cross Price Elasticity Formula above:

(542-550/550*100) / (140- 100/100 *100)

= -1.45/ 40

= -0.04

(ii) Using your answer for b. (i), explain the relationship between Good X and Good Y.

(Substitute, Complement etc)

From the answer above, it can be said that Goods X and Y are compliments of each other.

They are compliments because the Cross price elasticity was a negative value i.e. -0.04

(iii) Determine the Cross-Price elasticity of demand (XED) between Good X and Good Z.

= 800- 2Px- 0.05Px -0.2Py + 4Pz + 0.01I+ 2A

; Pz= $40, , P= $120,

Therefore when Pz = $50

-2(120)-0.05(14400)-0.2(140)+4(50)+0.01(7000)+2(250)

When Pz = $40 ,

and , when Pz = $50 ,

Therefore cross elasticity of demand = (590-550/550*100) /(50-40/40*100)

=727/25

=0.29

Cross Elasticity of Demand between Goods X and Z = 0.29


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(iv) Using your answer for b. (iii), explain the relationship between Good X and Good Z

(Substitute, Complement etc)

From the above answer it can be said that goods X and Z are substitutes because the cross price

elasticity was a positive figure i.e. 0.29

(v) Based on the solutions for parts b. (i) to (iv) above, suggest one example of an actual

agricultural product that fits the description for each of the following: Product X, Product Y

and Product Z.

Good X is Wheat and Good Y is Flour. These two are compliments to one another. Furthermore

if there is an increase in price for Wheat, the price of flour will increase and the quantity

demanded will decrease, therefor from the function it can be said that Good Z could be a

substitute for good X and an example for this will be rice because both are staple foods.

c. Consider the following two situations:

Both situations highlighted above, will affect the Total Revenue earned by Producers of Good X.

Explain which situation is more beneficial, to the producers of Good X, from a Total Revenue

earned perspective.

Situation 1; A 15% increase; 0.29*(15/100)= 0.0435

= 0.0435*550

Quantity = 23.93


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Therefore Total revenue= Price *Quantity

=23.93 * 40

=$957.2 is the total revenue for good Z

Situation 2; A 60% decrease ; -0.04*-60%=0.024

Quantity =0.024*550= 13.2

Therefore Total Revenue= 13.2*100

=$1320 is the total revenue for good Y

Situation 2 will be more beneficial to the producers of good X because as we can see the total

revenue earned for situation 2 which is Y was $1320 as opposed to situation 1 which the total

revenue earned was $957.2. As there was a 60% decrease in the price of good Y, there was a

greater quantity demanded so therefore a greater overall revenue compared to good Z. Simply

put more buyers will be attracted to the cheaper good than the expensive.

d. (i) Calculate the Income elasticity of demand (YED) for Good X

= 800- 2Px- 0.05Px -0.2Py + 4Pz + 0.01I+ 2A

-2(120)-0.05(14400)-0.2(140)+4(50)+0.01(8000)+2(250)

= % change inquantity demanded/ % change in income= (YED)

Therefore; (560-550/550*100)/(8000-7000/7000*100)

=1.82/14.30

=0.13


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(ii) Explain whether Good X is a normal good or an inferior good.

Income elasticity of demand for good X=0.13. Since this is a positive value, good Y is a normal

good.

e. Assume that the own Price elasticity of demand (PED) for Good X is -2 and the Income

elasticity

of Demand (YED) for Good X is 3.

(i) Calculate the percentage change in consumption that will occur, when income declines

by twenty percent (20%) .

Income Elasticity declines by 20% then YED= % change of demand/ -20% (a minus is used

because it is a decline) = 3

YED= 3

Therefore % change in demand= -20%*3= -60%

So when income declines by 20% the % change in consumption is decreased by 60%

(ii) Using the demand function presented for Good X above, determine the new quantity of

Good X demanded when income declines by twenty percent (20%) , and the Income

Elasticity of Demand (YED) for Good X is 3

Income =$7000

-2(120)-0.05(14400)-0.2(140)+4(50)+0.01(7000)+2(250)

When income =$7000 the quantity demanded= 536

Therefore the quantity demanded of good X demanded when income declines by 20% is 536.


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f. Suppose that the Cross-price elasticity of demand (XED) between Good X and Good Z is 4.

(i) How much would the price of Good Z (Pz) have to change in order to increase the

consumption of Good X by twenty five percent (25%)?

If n*2 (XED)= 4 and % change in X demanded=25%

Then XED= 25%/ % change in price of good Z=4

Therefore price of good Z would have to change 25%/4= 6.25%

Price of good Z would have to increase by 6.25% in order to increase the consumption of good X

by 25%.

(ii) Use a well-labeled illustration of the demand curve for Good X to show the effect on the

demand for Good X, of the change in the Price of Good Z (Pz) as calculated in f. (i)above.

Demand Curve showing the effect on demand for good X, of the change in the price of good Z

Price of good X

Quantity of good X Demanded

The graph illustrates rise in price of product X substitutes to shift the demand curve for productX to the right, hence more of product X will be purchased at each price, therefore the quantitydemanded will increase.

The Demand Function for Product X is Given By

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