Question

1. Imagine that the market for hotel rooms in Hotel California is perfectly competitive. In a typical day hotel rooms go for $100, and 1000 rooms are rented.
   1. To raise revenue, the mayor of Hotel California decides to charge hotels a lump sum tax per rented room (a lump sum tax is a set dollar amount per room rented). After the tax is imposed, the going rate for hotel rooms rises to $108, the after-tax money received by hotels for a room falls to $98, and the number of rooms rented falls to 900. How much is the lump sum tax? Calculate the amount of revenue this tax raises for Hotel California and the deadweight loss of the tax

Tax Revenue =_________

DWL =_________

2. What is the tax incidence on buyers of hotels rooms as a percent of the total tax revenue? What can you say about how elastic demand is relative to the elasticity of supply given your answer? Support your answer

Tax Incidence =_________

3. Now suppose the mayor increases the tax to $20. The price rises to $116, and the number of rooms rented falls to 800. Calculate the tax revenue and deadweight loss associated with this new tax.

Tax Revenue =_________

DWL =_________

4. Does the tax revenue rise in proportion with the tax rate increase? Does deadweight loss change in proportion with the tax rate increase? What can you infer about the relationship between tax revenue and the inefficiency created by a tax as the tax rate increases?

5. Now imagine that the mayor needs to generate a fixed amount of tax revenue for a community improvement project. She has the ability to place taxes on the market for hotel rooms and the market for restaurant meals. Suppose that demand and supply are relatively more inelastic in the market for hotel rooms. If she wants to do this in a way that minimizes the loss of market efficiently created by the taxes, how should she spread the tax over the two markets? Only tax hotels? Only tax restaurants? Some combination? Give your answer with no more than three sentences.

Answer 1

e the market that the in for hotela Imagine hotel rooms in hotel California is Putectly live ; on a typical day hotel rooms go and 100 rooms are rented. in rent = $ 100 and equilibrium competitive for ie $100 and in equilibrium rent hotel room = 100 room 9 Rent aby (52) . 108 A 100at I 90 Demand 0 .9.00 1000 hotel rooms a To raise revene the mayor of Hotel .. California decids to Charge hotels a luip sm - t are pu rented room. Hence the supply emuc : will shift up ward by the amont of tan : 7btn tan imposed, conswers are paying $ 108 hotele is setau receiving = $98, room rented balls to goo. S Scanned with 3 CamScanner

Huce amount of tau = (after tan price paid by consmens-afte tau rent received by hotels) =$(108-99) = $10 Hunce lemp- sum tan is (410] Amont of the sevene = Area of O ABID. = $(108-487 (900 -0)] Tan revene 1$ 9,000 Amount of deadweight loss = Area of A BCE = I x base x height .:=x (1600-900) *( 108-98) DW2 = $50 as now, tad portion of tau reveme . . generated from the eonsmes is - Area of T ABFU (900-0) (108-100) CS Scanned. with: < $ 7200 CamScanner

entracted Total reve me = $ 9000 Hace 100 x 100) or 80% of the so % of an is boren by the . 17200 une ( 9000 o tau revene or 80%. a consum. from consumers. onsiness.. ! Now, af to tau price paid by consuens. = $ 108 = Pz betore tan equilibrium Price = $ 100 = pi before tan, equilibrium room = Q1 = 1000 aftn t an equilibrium room - Q2 = 900 Hunce Price elasticity of demand Q2-Q1) x100 :Eda (P2-P1) X100 (P2tP1) ? 1900-1000) ico Taroot1ooo) - 10.53 2 > 7. đo 8- 10) x ( 11087100) -1.37 : Scanned with CamScanner

Before tau equilibrium Price Pi= $100. . afan dan rent se ceived by hotus P2 =$98 before tan equilibrium hotel room Q1 = 1000 aftri dan equilibrium hotel rooms Q2 = 900 I Huce elasticity of supply! (Q2-Q1) x100 QQ2+Q1 2 (P2-A) -X1.00 (putri) 1900-1000) Toot1000) 2 (98- 100) (98+10) * - 10.53 : -35.3 . - 2:0 - the as elasticity of supply i. e Es is greaty then the absolute value of elasticity of demand ) Edl ie 1:37. hence supply ed with CamScanner

ore elastic elastic is more compared to is heavily demand and fall on the we know know that tau side of the market which is less elastici hence here to consmens pay large portion Tie 80% of the tan compared to hotels paid by paid by hotels af in the impost al Now suppose the mayor increases the tax to $20 The price risu to $116.ie $.(1.6-100) = $16 out of $20 tan is : paid by consucess. The rest of $ (20-16) = $4 sam is paid by hotels. hence the rent received $ (100-4) = $96 af in the imposition of tan. and umby of rooms rented falls to 800... Hence the supply enve shifts upward from si to sa by the amount of tau ie by $20. -S2 and um by ubbly envere by 42 1 rent . 116A and 1000 . 800 man by of Scanned with CamScanner

Now tan reveme = Area of Ū ABCD ... (800-0) *(116-96) = $ 16,000 Deadweight loss = Area of A B C E = 1 x base x height - 1 x (1000-80) X(116-96) A DWL F $ 2,000 ä. As tau rate increases tion $ 10 to $20 tau revene increases from : a $9000 to $ 16,000 ie as a tan rate increases from $10 to $20 ie: 100% increase in tau rate increases tau revene from $9,000 to $ 16,000 le tan revenice increasu by (16,000-900) lo . 9ooo - 77.8 %0 . Huce increase in tem rate 100% increases tan reve me by 77.8% banned with CamScanner

Proportion with the sod Hua, tan revene is not rising en orton with the tax rate increase As tan increase by 100% as it increase . tiom & 10 to $20, deadweight loss increase from $500 to $2000 ie dead weight loss.is increasing by (200-500 100 = 300% Hince dead weight loss is rising more than proportionately with resing dan rate. Huce, as fan sate increases by 100%, tai revene rises by 77.8% Whereas deadweight loss is increasing by 3 00%. Hence the tau rate to increasis more in efficiency or deadweight loss and comparatively low levie of tau reveme Scanned with CamScanner