Question #59681

Suppose the initial price of apples is $1 per lb. and the price of orange is $2 per lb. A typical consumer has income $10 and spends all his income on the two goods. The consumer buys 4 lbs of apples at the initial price levels. Later the price of apples increases to $2 per lb and the price of orange remains unchanged, and the consumer buys 3 lbs apples. Based on indifference/budget constraint knowledge, derive the demand curve for apples. Make sure you label all the prices and quantities carefully. (Hint: calculate the quantities demanded for oranges in the 2 circumstances first.)

Expert's answer

Pa1 = $1 per lb, Po1 = Po2 = $2 per lb, I = $10, Qa1 = 4 lbs, Pa2 = $2 per lb, Qa2 = 3 lbs.

Based on indifference/budget constraint knowledge, I = Pa*Qa + Po*Qo, so before the change in price:

$1*4 + $2*Qo1 = 10,

Qo1 = 3 lbs.

After the increase in price:

$2*3 + $2*Qo2 = 10,

Qo2 = 2 lbs.

So, we have two points from the demand curve for apples: Pa1 = $1, Qa1 = 4 lbs, Pa2 = $2, Qa2 = 3 lbs.

In this case equation of demand curve using the equation of the line is:

(P - 1)/(2 - 1) = (Q - 4)/(3 - 4),

P - 1 = 4 - Q,

P = 5 - Q - the equation of demand curve for apples.

Based on indifference/budget constraint knowledge, I = Pa*Qa + Po*Qo, so before the change in price:

$1*4 + $2*Qo1 = 10,

Qo1 = 3 lbs.

After the increase in price:

$2*3 + $2*Qo2 = 10,

Qo2 = 2 lbs.

So, we have two points from the demand curve for apples: Pa1 = $1, Qa1 = 4 lbs, Pa2 = $2, Qa2 = 3 lbs.

In this case equation of demand curve using the equation of the line is:

(P - 1)/(2 - 1) = (Q - 4)/(3 - 4),

P - 1 = 4 - Q,

P = 5 - Q - the equation of demand curve for apples.

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