Question

There are 10,000 identical individual buyers in the market for commodity X, each with a demand function given by Qdx = 12 – 2Px and 1,000 identical producers of commodity X, each with a supply function given by Qsx = 20Px.
(i) Find the market demand function and the market supply function for commodity X.
(ii) Obtain the equilibrium price and equilibrium quantity.
(iii) Suppose the government decides to collect a sales tax of Rs 2 per unit sold from each of the 1,000 sellers of commodity X. What effect will this have on the equilibrium price and quantity of commodity X?

Answer 1

b) The subsidy of 1 changes the supply equation to S = 20(P+1). This is true since the subsidy effectively increases the producers selling price by 1. 
Then 20*1000(P+1) = 10000(12-2P) is the equilibrium equation. 
Now the equilibrium price is 2.50 and the quantity is 70000. Consumers gain here since the price is lower. However since consumers support the subsidy by making tax payments to the government, in this case $70000, the net result is negative for consumers as a group. Consumers with a lower tax rate and higher consumption will benefit most from a subsidy, but here you are not supposed to consider taxes I think. 
c) The sales tax is paid by the consumer so the demand equation changes to 
D = 12 -2(P+2). 
The equilibrium equation becomes 10000(12-2(P+2)) = 20*1000*P. 
The equilibrium price is 2 and the quantity 40000. The total price is 4 for the consumers due to the tax. The total tax collected is 2*40000 = $80000.

Answer 2

Answer:

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