Suppose that there are two goods x1 and x2 Suppose that the

Suppose that there are two goods, x1 and x2. Suppose that the initial prices are given p1 = 1 and p2 = 2 and the income is given 100. There are two possible policies that the government is considering:

Policy 1 is a bulk penalty only on good 1, because any consumption more than 80 units of good 2 generates some negative impact on the economy, say, pollution or conges- tion. So, for each additional unit of x1 more than 80, the new price of $2 will be applied.

Policy 2 is a bulk discount only on good 2. For each additional unit of x2 more than 20, the new price of $1 will be applied.

(1) Suppose that only Policy 2 is implemented. Write down the budget set and draw it in a graph. (hint: write down the budget sets for two separate cases: (i) 0 ? x2 ? 20 and (ii) x2 > 20)

(2) Suppose that both of Policy 1 and Policy 2 are implemented at the same time. Write down the budget set and draw it in a graph. (hint: write down the budget sets for four separatecases: (i) 0?x1 ?80 and 0?x2 ?20, (ii) 0?x1 ?80 and x2 >20, (iii) x1 >80 and 0?x2 ?20,and (iv) x1 >80 and x2 >20)

Solution

P1x1+P2x2 = 100

P1 = 1 and P2 = 2

1) Applying policy 2

the budget set will be

2. (i) In this case P1 = 1 and P2 =2 the possible sets are (80,10), (78,11), (76,12)..............(60,20)

(ii) In this case P1 = 1 and P2 =1 the possible sets are (79,21), (78,22), (77,23)..............(0,100)

(iii) In this case P2 = 2and P1 = 2 the are no possible sets.

(iv) n this case P1 = 2 and P2 =1 the are no possible sets