Consider a competitive industry producing a product at a marginal cost of 5. Inv

Question

Consider a competitive industry producing a product at a marginal cost of 5. Inverse demand in this industry is given by
P (q) = 15 - 2q

(i) What is the competitive equilibrium price?

Assume now that every unit of output creates pollution which creates a marginal damage which is increasing in output: the marginal damage function is
MD = 1 + q

(ii) What is the socially optimal output?

(iii) Suppose you consider introducing a unit tax t on output. Call t is the value of t the unit tax that would lead Örms to produce the socially e¢ cient output? Which of the following is true: t = 1; t < 1; t > 1?

(iv) What is the exact value of t?

(iv) What is the revenue from this tax?

Explanation / Answer

For a competetive firm: Price= Marginal revenue= Marginal Cost P=MR=MC MC=$5 Given: P= 15-2q Profitmaximizing quantity is produced when MR=MC. MR=P=15-2q MC=5 this implies: 5=15-2q 2q=15-5 2q=10 q=10/2 q=5 Equillibrium quantity= 5 units. If we substitite in the inverse demand function we can get equillibrium price. P= 15- 2(5) = 15 - 10 P=$5 Equillibrium price= $5 (ii) What is the socially optimal output?
Social optimu quantity is found when Marginal social cost is in equilibrium with Marginal benifit. Marginal Social cost= Marginal Damage= MD= 1+q Marginal benefit= MR=P= $5 ( for a competetive firm marginal benifit received is equal to price which is equal to marginal cost) So, social optimum output is achieved when, MD= P MD= 1+q P= $5          1+q = 5              q = 5- 1                 =4              q= 4 units Socially optimum output is 4 units.         
(iii) Suppose you consider introducing a unit tax t on output. Call t is the value of t the unit tax that would lead firms to produce the socially e¢ cient output? Which of the following is true: t = 1; t < 1; t > 1?
If we want to introduce a tax, t and this should limit the output to social optimumlevel, which is 4 units. than the condition for this is. P+t= 15 - 2q price is market equilibrium price= $5 q should be social optimum output= 4 units. Substituting in the above inverse demand function we get, 5 +tax= 15 -2 (4)      tax= 15 - 8 - 5          = $2       Tax= $2 which is greater than 1
(iv) What is the exact value of t?
Tax= $2
(iv) What is the revenue from this tax? Revenue from tax, Units sold is 4units revenue earned= 4 units x tax                       = 4 x $2                       = $8 Tax revenue= $8. (ii) What is the socially optimal output?
Social optimu quantity is found when Marginal social cost is in equilibrium with Marginal benifit. Marginal Social cost= Marginal Damage= MD= 1+q Marginal benefit= MR=P= $5 ( for a competetive firm marginal benifit received is equal to price which is equal to marginal cost) So, social optimum output is achieved when, MD= P MD= 1+q P= $5          1+q = 5              q = 5- 1                 =4              q= 4 units Socially optimum output is 4 units.         
(iii) Suppose you consider introducing a unit tax t on output. Call t is the value of t the unit tax that would lead firms to produce the socially e¢ cient output? Which of the following is true: t = 1; t < 1; t > 1?
If we want to introduce a tax, t and this should limit the output to social optimumlevel, which is 4 units. than the condition for this is. P+t= 15 - 2q price is market equilibrium price= $5 q should be social optimum output= 4 units. Substituting in the above inverse demand function we get, 5 +tax= 15 -2 (4)      tax= 15 - 8 - 5          = $2       Tax= $2 which is greater than 1
(iv) What is the exact value of t?
Tax= $2
(iv) What is the revenue from this tax? Revenue from tax, Units sold is 4units revenue earned= 4 units x tax                       = 4 x $2                       = $8 Tax revenue= $8.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.