Question

Consider an example of the  market; if the supply and demand represented as:

Qs = - 200 + 4p ;  Qd = 800 – p

Solve:

a)      Equilibrium price and equilibrium quantity and calculate total revenue?

b)     If there were a price celling equal to 250 per each cloth imposed, calculate the price elasticity of demand? Does this consider elastic, inelastic or unit elastic?  Also, calculate the total revenue?

c)      Now consider the shoes market; if the supply and demand is:

 i.        Qs = -100 + 3p ; Qd = 800 – 6p, calculate the equilibrium price and equilibrium quantity.  Also, calculate Total Revenue.

 ii.        If there were a price celling of 120  imposed per each pair of shoes, calculate the price elasticity of demand? Does the shoes consider elastic, inelastic or inelastic or unit elastic? Also calculate total revenue. 

 

d)       Compare the total revenue for the clothing market and the total revenue you found on the clothing market.  Which one of product’s total revenue has been increased after the price have been increase and why?

e)       Recall part a (the cloth market) Calculate the CS & PS.

f)        Now, if the government impose sales tax equal to 12.5% on cloth, what is the CS, PS, government revenue, DWL and show this on the graph?

g)       Without calculation, would you expect to have higher/ lower government revenue and DWL on shoes and why?

Answer 1

a.       We have,

At equilibrium,

Q_S = Q_D

- 200 + 4p = 800 – p

5p = 1000

P = 200  ,  Q = 800-200 = 600

Total Revenue = 200*600 = 120000

 

b.      We have,

At P = 250

Q_D = 800 – 250 = 550

Price elasticity of demand = ((550-600) / 600) / ((250-200)/ 200)=

-(50/600)/(50/200)=.083/.25= .332

As .332 < 1, demand is inelastic

Total Revenue= 250*550= 137500

 

c.        

i.                    We have,

At equilibrium,

Q_S = Q_D

-100 + 3p= 800 – 6p

9p = 900

P = 100 , Q = 800-6*100=200

Total Revenue = 100*200 = 20000

ii.                  At P = 120,

Q = 800 – 6*120 = 80

Price elasticity of demand = (80 - 200)/200/(120 - 100)/ 100

= - (.6\ .2) = -3

As 3 > 1, demand is elastic.

Total Revenue = 120*80 = 9600

 

d.      As shown in previous clothing market’s revenue has increased after the price increase and shoes market’s revenue has decreased. Clothing’s revenue before and after the price increased from 120000 to 137500 and shoe’s revenue decreased from 20000 to 9600.

This is because clothing’s demand is inelastic and hence, % decrease in quantity demanded is lesser than the % increase in price. While battery’s demand is elastic and hence, % decrease in quantity demanded is higher than the % increase in price.

 

 

e.       For clothing market When -200+4p=800-p

QS=0 , P =50

When QD = 0 , P = 800

CS=(800 - Peq)*Qeq/2 = (800 – 200)*600\2 = 180000

PS = (Peq - 50)*Qeq/2= (200-50)*600\2 = 45000

 

f.        We have

P^B = 220

P^S = 195

Plug P = 220 on the demand curve or P = 195 on the supply curve, you will get Qd = Qs = 580.

Qd = 800 – p

Qd = 800 – 220

Qd = 580

OR Qs = - 200 + 4p

Qs = -200 + 4(195) 

Qs = 580

CS = {(800 - 220)* 580 * ½ = 168,200 .

PS = {(195 – 50) * 580 * ½ = 42,050 

Tax Revenue = (220 – 195 ) * 580 = 14,500 .  OR: (200 * 12.5 %) * 580 = 14,500 .

Total surplus = 168,200 + 42,050 SAR + 14,500 = 224,750 

DWL = {(220 – 195) * (600 – 580)} * ½ = 250.

Or DWL = previous total welfare (before tax) – new total welfare (after tax) = 225,000 – 224,750 = 250

g.       As shown above, shoes' demand is elastic. So, quantity of shoes demanded will fall substantially because of the price increase caused by taxes. Therefore, government revenue will be lesser and deadweight loss greater for the shoes market than for the clothing market.