Question

Demand: P = 100-2Qd+I

Supply: P = 15 + 3Qs

Suppose that consumer income (I) is 15. Using excel plot how the tax revenue changes as T increases. HINT: Revenue will be on your y axis and the tax (0,1,2,3,…) will be on your x-axis.  Find the revenue maximizing tax. What would be the tax revenue generated and the quantity of goods sold at this tax rate.

Answer 1

Here the market demand and supply are “P = 100 – 2*Q + I = 100 – 2*Q + 15”, => P = 115 – 2*Q. The market supply is, “P = 15 + 3*Q”. Let’s assume a quantity tax of “t” per unit is imposed on the producer, => the new supply function is given by, => “P = 15 + t + 3*Q”. At the equilibrium the demand must be equal to supply.

=> Pd = Ps, => 115 – 2*Q = 15+t+3*Q, => 100 – t = 5*Q, => Q = [100-t]/5, => Q = 100/5 - t/5.

=> Q = 20-t/5. So, the tax revenue is given by.

=> T = t*Q = t*(20-t/5) = 20*t – t^2/5, => T = 20*t – t^2/5.

                              

So, here for “t=50” the tax revenue is maximum. So, the tax revenue maximizing tax is “50”.