# Question: jack likes both apples and bananas he consumes nothing else...

###### Question details

Jack likes both apples and bananas. He consumes nothing else.
Jack consumes x_{1} bushels of apples per year and
x_{2} bushels of bananas per year. Suppose that Jack’s
preference is represented in the following utility function:
u(x_{1}, x_{2}) = x_{1}x_{2}.
Suppose that the price of apples is $2, the price of bananas is $3,
and Jack’s income is $50.(Only one diagram is necessary for this
entire problem)

1. What’s the equation for Jack’s budget constraint? Draw it in a diagram. Plot a few points on the indifference curve that gives Jack a utility of 150 and sketch this curve. Now plot a few points on the indifference curve that gives Jack a utility of 100 and sketch this curve. Can Jack afford any bundles that give him a utility of 150; what about a utility of 100? On your graph, mark a point that Jack can afford and that gives him a higher utility than 100. Label that point A.

2. What is the marginal utility for the apples? What is the marginal utility for the bananas? Using marginal utilities, find Jack’s marginal rate of substitution.

3. What is the slope of Jack’s budget line? Using this and the marginal rate of substitution, derive the function for a Engle’s curve, which implies the optimal choice: an equation that implies that the budget line is tangent to an indifference curve. Draw it out.

4. The best bundle that Jack can afford must lie somewhere on the line you just penciled in. It must also lie on his budget line. On your graph, label this best affordable bundle with an E. What’s the best bundle equal to?