Answer to Question #291206 in Macroeconomics for YENEW

Question

Given Demand Function Qd=40-2p And Supply Function 2p-Qs=20 Assume The Gov.T Increase Atax Of T Per Unit On Quantitiy Supplied And The Producer Adjust The Supply Function To Include The Tax

 

A) Find The Tax Rate At Which Tax Revenu Is Maximum?

B) Find The Maximum Revenu Which Can Be Obtained From A Function?

Answer 1

$Q_d=40-2p$ (1)

Therefore, $p=20-\frac{Q_d}{2}$

$2p-Q_s=20\\ p=10+\frac{Q_s}{2}$

$P_t=$ Supply function after the imposition of tax

$P_t=(10+\frac{Q_s}{2})+t$

In equilibrium, $Q_d=Q_s=Q$

$p=P_t\\ 20-\frac{Q_d}{2}=(10+\frac{Q_s}{2})+t\\ Q=10-t$

$GR=Q\times t\\ GR=(10-t)t=10t-t^2\\ \frac{d(GR)}{dt}=10-2t=0\\ \implies t=5\%$

b.)

$R(p)=p \cdot Q_d\\ R(p)=p(40-2p)\\ R(p)=40p-2p^2\\ \frac{dR(p)}{dp}=40-4p=0\\ p=10 \text{ is the maximum}$

The maximum revenue is $R(10)=40(10)-2(10)^2=200$