Exercise 1

Gentle Charlie consumes only apples and bananas. His utility function is U(xA ,xB ) = xA xB   (where xA  and xB  are the number of apples and bananas consumed in a day). The price of apples is $1, the price of bananas is $2, and Charlie’s income is $40 a day. The price of bananas suddenly falls to $1.

(a) How many apples and bananas did Charlie consume per day before the price change? On a graph below, use black ink to draw Charlie’s original budget line and put the label A on his chosen consumption bundle.

(b) If, after the price change, Charlie’s income had changed so that he could exactly afford his old consumption bundle, what would his new income have been? With this new income and new prices, how many apples and bananas would Charlie consume? Use red ink to draw the budget line corresponding to this income and these prices. Label the bundle that Charlie would choose at this income and the new prices with the letter B.

(c) Does the substitution effect of the fall in the price of bananas make him buy more bananas or fewer bananas? What is the exact amount of the change in the amount of bananas consumed?

(d) After the price change, how many apples and bananas does Charlie buy?  Use blue ink to draw Charlie’s actual budget line after the price change.  Put the label C on the bundle that he chooses after the price change. Draw three horizontal lines on your graph, one from A to the vertical axis, one from B to the vertical axis, and one from C to the vertical axis. Along the vartical axis, label the income effect, the substitution effect, and the total effect on the demand for bananas. Is the blue line parallel to the red line or the black line you drew before?

(e) Is the income effect of the fall in the price of bananas on Charlie’s demand for bananas the same as the effect of an increase, or a decrease in Charlie’s income? By how much would his income have to increase/decrease to have the same effect? Does the income effect make him consume more bananas or fewer? How much is the change in consumption of bananas?

(f) Does the substitution effect of the fall in the price of bananas make Charlie consume more or fewer apples? How many more/fewer apples does Charlie consume? Does the income effect of the fall in the price of bananas make Charlie consume more or fewer apples?  What is the total effect of the change in the price of bananas on the demand for apples?