Question

Goods 1 and 2 are perfect complements for Kane. He always consumes these two goods in the ratio of 2 units of good 2 for every unit of good 1. The price of good 1 is $1.00, and the price of good 2 is $4.00. Kane has $936.00 to spend. part 1) The substitution effect of a change in the price of good 2 from $4.00 to $6.00 will reduce the demand for good 2 by _______ units. part 2) The income effect of the increase in the price of good 2 from $4.00 to $6.00 will cause demand for good 2 to fall by ________ units..

Answer 1

(a) The good 1 and good 2 are perfect complementary goods for the Kane. We assume Good 1 as (x) and good 2 as (y) for simplicity. The utility function and budget constraint would be:

• We are provided following budget constraint:
• Solving the above equation for the optimization and find optimal bundles at the initial price level (1,4)

• Putting above in the budget constaint, we find optimal bundles as

• At the old price level (1,4) the optimal bundles are (104,208)

Now, price of good 2 (y) increases from the $4 to $6. The new prices are then (1,6). We shall find optimal bundles from the new price level.

• Thus, at the new prices, the optimal bundle for both goods are (72,144).

Now we know that when the goods are perfect complements, the substitution effect of a price change is zero. Therefore, there exist the income effect which is equal to the total change from new to old bundle.

The demand for good 2 declines from