In: Economics
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:
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?
a. We have,
At equilibrium,
QS = QD
- 200 + 4p = 800 – p
5p = 1000
P = 200 , Q = 800-200 = 600
Total Revenue = 200*600 = 120000
b. We have,
At P = 250
QD = 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,
QS = QD
-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
PB = 220
PS = 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.