Suppose the market for cigarettes is characterized by the following information:

Question

Suppose the market for cigarettes is characterized by the following information:
Qd = 70 – 5P [Demand] Qs = 3P – 10 [Supply]
Suppose the government imposes a sales tax of $2 per unit. Answer questions (i) through (v) below:
i) Calculate the magnitude of the consumer surplus and producer surplus in the pre-tax equilibrium.
ii) Calculate the tax revenue in the post-tax equilibrium.
iii) Calculate the change in consumer surplus due to the sales tax.
iv) Calculate the change in producer surplus due to the sales tax.
v) Calculate the Dead-Weight-Loss due to the sales tax.
[Note: P = price per unit; Qd = thousands of units demanded; Qs = thousands of units supplied]

Explanation / Answer

Graph out Qs and Qd. It helps with the analysis. i). FInd pre tax equilibrium. Set Qs=Qd. U will get p=10 and q= 20. Once u have this numbers, u can find consumer and producer surplus. Hint: Prod surplus is the area of the triangle from market price to the max. price where consumers are willing to pay. Producer surplus is the triangle area where the market price is up to the minimum price where producers are willing to produce. COnsumer surplus= 1/2 * (14-10)*20= 40 Prod. surplus= 1/2 (10-10/3)*20= 400/6 ii).Tax revenue. To calculate this, you have to find the new quantity ssupplied and quantity demanded after tha tax of 2 dollars is imposed.After a tax is imposed, the price consumers pay will shift to P +1 and the price producers receive will shift to P-1. The consumers' price will be equal to the producers' price plus the cost of the tax. Another words, the price difference between producers and consumers= 2. At 11 dollars, Qd= 15. Or conversely, at 9 dollars( producers new price after tax), Qs=17. Tax revenue= (1 * 15)+( 1* 17)= 32. iii). FInd the new surpluses. Producers surplus after tax=1/2( 9-10/3)*17= 289/6. The change is simply take the surplus before tax- surplus after tax= 400/6-289/6= 111/6 Do the same to find the change in consumer surplus. Consumer surplus after tax= 1/2 * (14-11)* 15= 45/2 Change in consumers surplus is = 40- 45/2= 35/2 v). calculate deadweight loss. dead weight loss is the sum of the two small triangles. It is easier if you graph this out. = 1/2 * 1 * (20-15) + 1/2 *1 * ( 20-17)= 1/2 * 5 + 1/2 * 3= 4.

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