(Solution) If You Do This, The Result Will Look Like: Assume(real)= Now The Program Knows That You Are Interested Only In Real Solutions. | Snapessays.com


(Solution) If you do this, the result will look like: assume(real)= Now the program knows that you are interested only in real solutions.


If you do this, the result will look like:

 

assume(real)= ?

 

Now the program knows that you are interested only in real solutions.

 

 

The demand function (absent taxes) is D=P^{-?} and the supply function is S^{?}. These are special functions, known as "constant elasticity" demand and supply. The parameter ? is the elasticity of demand and the parameter ? is the elasticity of supply. For "most" functions (including the linear functions we worked with above) the elasticity of demand or supply changes with the price at which the function is evaluated. The constant elasticity functions are special: for those functions, the elasticity does not change with the price at which the function is evaluated.

 

For this particular nonlinear model, it is convenient to work with ad valorem rather than unit taxes. If a producer (for example) pays an ad valorem tax of ? and if the market (i.e. consumer) price is P, the producer pays the tax ?P on each unit sold, so her after tax revenue per unit sold is P(1-?).

 

 

The unit tax t that is equivalent to an ad valorem tax ? depends on the market price, P; that is, t=?P.

 

 

If consumers pay an ad valorem tax ? and the market (i.e. producer) price is P, a consumer pay a tax ?P on each unit sold, so her tax-

 

Now define the tax-inclusive supply and demand functions

 

S=(P(1-?))^{?}

 

D=P^{-?}

 

Unfortunately SN cannot find the equilibrium price, but it is easy to do this "by hand". (This limitation is due to the mathematics package MuPad. Older versions of this product supported a different mathematics package, Maple, which does not have this kind of limitation.) At the equilibrium price, D=S, or

 

(S/D)= P^{?}(-P(?-1))^{?}=1

 

which implies

 

P^{?}(P(1-?))^{?}=1

 

P^{?+?}=(1-?)^{-?}

 

P=(1-?)^{-(?/(?+?))}

 

This expression gives the equilibrium price as a function of the ad valorem tax, ?

 

9. What is the equilibrium price under a 0 tax (?=0)? Denote this price as ?

 

Recall that the tax incidence for consumers is the ratio of the increase in the price that consumers pay (P-?) to the unit tax (?P), and the tax incidence for producers is the ratio of the decrease in the price that producers receive (?-(1-?)P) to the unit tax (?P).

 

 

Q) could you please figure out problem no.9 ? the question is located above from here. Thank you so much !

 


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This question was answered on: May 23, 2022

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