Question

In: Economics

An industry's inverse demand was PD = 20 - 0.1Q and its inverse supply was PS...

An industry's inverse demand was PD = 20 - 0.1Q and its inverse supply was PS = 4 + 0.1Q.

a. Calculate the consumer surplus, producer surplus, government revenue and deadweight loss for taxes of $4, $8, $12 and $16 per unit sold.

b. Graph government revenue and deadweight loss as functions of these tax rates.

c. What tax maximizes government revenue?

Solutions

Expert Solution

Inverse demand function, P = 20 - 0.1Q

Inverse supply function, P = 4 + 0.01Q

At equilibrium supply and demand are equal.

20 - 0.1Q = 4 + 0.1Q

=> 0.1Q + 0.1Q = 20 - 4

=> 0.2Q = 16

=> Q = 80 units

P = 20 - 0.1× 80= $ 12 per unit

When tax = 0

Consumer surplus =(1/2)*(20-12)*80 = $ 320

Producer surplus = (1/2)*(12-4)*80 = $ 320

Government revenue = 0

Dead weight loss = 0

When government imposes a tax of T then the price paid by buyer will be greater than price received by sellers. Let P be the price paid by buyer and Ps price received by seller. Then, Ps = P -T.

When a tax of $ 4 is imposed

Supply curve , P - 4 = 4 + 0.1Q

P = 8 + 0.1Q

Equate it to demand curve

P = 20 - 0.1×60 = $ 14

CS = (1/2)*(20-14)*60 = $ 180

PS =(1/2)*(10-4)*60 = $ 180

Government revenue = 4 × 60= $ 240

Dead weight loss = (1/2)*(4)*(80-60) = $ 40

When tax = $ 8

New supply curve P = 12 + 0.1Q

Price paid by buyer, P = 20 - 0.1×40 = $ 16 / unit

CS=0.5×(20-16)×40 = $ 80

PS = 0.5×(8-4)×40= $ 80

Government revenue =8×40 =$ 320

Dead weight loss =0.5×8×(80 - 40) =$ 160

Now when tax = $ 12

New supply curve P = 16 + 0.1Q

Price paid by buyers, P = 20 - 0.1×20 = $ 18

Price received by sellers = 18 - 12 =.$ 6

CS = 0.5×(20-18)×20 = $ 20

PS=0.5 ×(6 -4) × 20 = $ 20

Government revenue = 12 × 20 = $ 240

Dead weight loss= 0.5× 12 × (80-20) = $ 360

Now when tax is $ 16

Q = 0

CS = 0

PS = 0

Government revenue = 0

Deadweight loss = 0.5×16 × 80 = $ 640

Now refer the graph for deadweight loss

C. Refer the graph for government revenue the tax is maximized at a tax of $ 8 per unit.

I have determined the values manually if any doubt kindly contact through comments will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.


Related Solutions

An industry's inverse demand was P^D = 20 - 0.1Q and its inverse supply was P^S...
An industry's inverse demand was P^D = 20 - 0.1Q and its inverse supply was P^S = 4 + 0.1Q. Calculate the consumer surplus, producer surplus, government revenue and deadweight loss for taxes of $4, $8, $12 and $16 per unit sold. Graph government revenue and deadweight loss as functions of these tax rates. What tax maximizes government revenue?
The market for a product has the following inverse demand and supply functions Pd= 120 -...
The market for a product has the following inverse demand and supply functions Pd= 120 - Qd Ps   = 0.5Qs. Suppose the state government levies a tax of $15 on each unit sold, imposed on the consumers. Find the prices that consumers pay (Pd) and the producers receive (Ps) and the new quantity traded in the market, Q**. Show on your diagram. What is the incidence of the tax on consumers and what on producers. How much money does the state...
The market for a product has the following inverse demand and supply functions Pd = 120...
The market for a product has the following inverse demand and supply functions Pd = 120 - Qd Ps      = 0.5Qs. 1. Find the equilibrium price P* and quantity Q*. Show on a diagram 2. Find the consumer and producer surplus
The market for a product has the following inverse demand and supply functions Pd = 170...
The market for a product has the following inverse demand and supply functions Pd = 170 - Qd Ps    = 20 + 0.5Qs Find the competitive equilibrium and show on a diagram. Find the consumer surplus and producer surplus. Suppose the government gives a per-unit subsidy of $15 to sellers on each unit sold. Find the new equilibrium (quantity traded, consumer and seller prices). Show on your diagram. What is the incidence of the subsidy on consumers and what on suppliers?...
1. Suppose demand is given by PD = 20 − .03QD and supply is given by...
1. Suppose demand is given by PD = 20 − .03QD and supply is given by PS = 6 + .04QS. Now suppose the government imposes a $3.5 tax on suppliers. a.) What is the total welfare? b.) What is the deadweight loss?
. Consider the following supply and demand system Supply: QS = 60 PS – 120 Demand:...
. Consider the following supply and demand system Supply: QS = 60 PS – 120 Demand: QD = 1080 – 40 PD For part a) of this question, find the equilibrium price and quantity. Calculate the Consumer Surplus, Producer Surplus, and Total Surplus at the free market equilibrium. For parts b) through e), consider the government price control described below for each part below. For each part, calculate the equilibrium price and quantity. Calculate the consumer surplus, producer surplus, total...
QUESTION 2 The supply and demand functions of a good are given by Ps =32 +...
QUESTION 2 The supply and demand functions of a good are given by Ps =32 + Q2S and PD= 140 - Q2D/3 where ?PS , ?PD, ?QS and QD  are the price and quantity supplied and demanded, respectively. a) Calculate the producer’s surplus and consumer’s surplus at the equilibrium point. b) Explain the effect, if any, on consumer’s surplus if the government imposes a fixed tax on this good (note: no calculation expected).
Question 1: For an industry, Qd = 40 – Pd and Qs = Ps.. Suppose the...
Question 1: For an industry, Qd = 40 – Pd and Qs = Ps.. Suppose the government imposes a price floor of $28. Complete the following table and explain how you derived your answers.                                                  No Price Floor                        Price Floor Consumer Surplus Producer Surplus _____________________________________________________________ Total Surplus Deadweight Loss
Suppose annual inverse demand and inverse supply for groundwater for irrigation purposes are given by the...
Suppose annual inverse demand and inverse supply for groundwater for irrigation purposes are given by the following equations, where ? is millions of acre feet of water: Demand: ? = 18 − 2Q/3 Supply: ?=1?/3 Draw the demand and supply curves. Compute the equilibrium quantity and price of water and indicate the equilibrium on the graph. Be sure to indicate the value of the vertical intercepts of the two lines. Label all the items in your diagram, especially demand, supply,...
. The (inverse) equations for the supply and demand for French Champagne are given below. Supply:...
. The (inverse) equations for the supply and demand for French Champagne are given below. Supply: P = 40 + ¼Q Demand: P = 100 – ½Q [Half point for each question] a) compute the equilibrium price and quantity of Champagne. b) Suppose and excise tax (i.e. a tax paid by producers) of $18 per bottle is imposed. What are the equations for the new supply and demand curves? What is the new EQ price and quantity? Specify what the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT