Question

In order to encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common practice by other firms is to offer “quantity discounts” to consumers who purchase large quantities of a good. Suppose income is $100, PX = $2 if the consumer buys less than 40 units of X, and PY = $5.

A. For the energy case, assume PX = $3 if the consumer buys more than 40 units of X

B. For the “quantity discounts” case, assume PX = $1 after 40 units of X were consumed

Draw the budget constraints in each of the cases above. What are the implications of the opportunity sets in terms of consumer behavior to consume each of the products?

Answer 1

a) If Px increases from $2 to $3, the maximum he can buy of good X decreases from 100/2 = 50units to 46.7 as the first 40 units at $2 ( means 100 - 40*2 =) $20 left, and 20/3= 6.7 ( means a total of 40 + 6.7 = 46.7 units.)

Py = $5 so maximum of y = 100/5 = 20 ( y intercept)

Budget line with price increase. The consumer should select indifference curves so that consumption of X decreases as price increases.

kink at 40 unit of X.

b) If Px decreases from $2 to $1, the maximum he can buy of good X increases from 100/2 = 50units to 60units as the first 40 units at $2 ( means 100 - 40*2 =) $20 left, and 20/1= 20 ( means a total of 40 + 20 = 20 units.)

Py = $5 so maximum of y = 100/5 = 20 ( y intercept)

Budget line with price decrease. The consumer should select indifference curves so that consumption of X increases as price decreases.

kink at 40 unit of X.

opportunity set—all possible combinations of consumption that someone can afford given the prices of goods and the individual's income.

the implications of the opportunity sets in terms of consumer behavior to consume each of the products is that consumer will choose that set which provide him / her the maximum uility among all of the opportunity set.