Suppose that a market is described by the following supply and demand equations:

Question

Suppose that a market is described by the following supply and demand equations: Qs = 2P Qd = 300 – P a. Solve for equilibrium price and quantity. b. Suppose that a tax of T is placed on sellers. What are the new supply and demand equations? Solve for the new equilibrium. What happens to price received by sellers, the price paid by buyers, and the quantity sold? (All variables should be given as a function of T.) c. Use your answer to part (b) to solve for tax revenue. Graph this relationship for T between 0 and 300. d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Solve for deadweight loss as a function of T. Graph this relationship for T between 0 and 300. e. Government now levies a tax on this good of $200 per unit. Is this a good policy? Why or why not? Can you propose a better policy?

Clearly graphed and explained answers will be appreciated greatly! Thank you!

Explanation / Answer

Setting amount supplied equivalent to amount requested gives 2P = 300 – P. Adding P to both sides of the mathematical statement gives 3P = 300. Partitioning both sides by 3 gives P = 100, which is the balance cost. Connecting P = 100 back to either mathematical statement for amount requested or supplied gives Q = 200 as the balance amount.

Presently P is the cost got by merchants and P+T is the cost paid by purchasers. Comparing amount requested to amount supplied gives 2P = 300 - (P+T). Adding P to both sides of the comparison gives 3P = 300 – T. Isolating both sides by 3 gives P = 100 - T/3. This is the cost got by merchants, and is obviously not exactly before the expense was forced. The purchasers pay a value equivalent to the cost got by merchants in addition to the duty (P+T = 100 + 2T/3). The amount sold is presently Q = 2P = 200 – 2T/3.

Since expense income is equivalent to T x Q and Q = 200 - 2T/3, charge income measures up to 200T - 2T2/3. Charge income is zero at T = 0 and at T = 300.

The zone of the triangle (laid on its side) that speaks to the deadweight misfortune is 1/2 x base x stature, where the base is the adjustment in the cost, which is the measure of the expense (T) and the tallness is the measure of the decrease in amount (2T/3). So the deadweight misfortune approaches 1/2 x T x 2T/3 = T2/3. This ascents exponentially from 0 (when T = 0) to 45,000 when T = 300.

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