ECON 203 – Suppose you are deciding whether to drive

ECON 203 – Suppose you are deciding whether to drive
. Suppose you are deciding whether to drive or take a bus to your parents’ home for Thanksgiving weekend. The bus ticket is $60. The bus ride and the car trip are the same length, but on the bus, you can get work done, totaling $40. (Assume the disutility of driving and working are the same.) The total fuel and maintenance costs if you drive are $30. (5 points) ?
a. Should you drive or take the bus? (2 points) ?
b. After buying the bus ticket, you realize it is only one-way. If the return ticket is ?also $60, should you take the bus? What if the return ticket is $90? (3 points) ?
2. Charlie likes both apples, x, and bananas, y. He consumes nothing else. Suppose that Charlie’s preferences are given by the utility function u(x,y) =xy. Suppose that the price of apples is $1, the price of bananas is $2, and Charlie’s income is $40. (14 points)
a. Draw Charlie’s budget line. Plot a few points on the indifference curve that gives Charlie a utility of 150 and sketch this curve. Now plot a few points on the indifference curve that gives Charlie a utility of 300 and sketch this curve. (3 pts) ?
b. Can Charlie afford any bundles that give him a utility of 150? Can Charlie afford any bundles that give him a utility of 300? (2 pts) ?
c. On your graph, mark a point that Charlie can afford and that gives him a higher utility than 150. Label that point A. (1 pt) ?
d. Neither of the indifference curves that you drew is tangent to Charlie’s budget line. Let’s try to find one that is. What is the marginal utility for the apples, !”, as ?!” ?a function of x & y? What is the marginal utility for the bananas, !”, as a function !” ?of x & y? Using marginal utilities, find Charlie’s marginal rate of substitution. (2 pts) ?
e. What is the slope of Charlie’s budget line? Set this equal to the answer to (d) and solve for y. This is the equation for Charlie’s income-consumption curve (the set of points on all indifference curves with slope equal to the price ratio). Each point on this curve corresponds to one point on every different indifference curve, all with the same slope. Draw a line that passes through all of these points. (2 pts) ?
f. The best bundle that Charlie can afford must lie somewhere on the income- consumption curve. It must also lie on his budget line. If the point is outside of his budget line, he can’t afford it. If the point lies inside of his budget line, he can afford to do better by buying more of both goods. On your graph, label this best affordable bundle with an E. At which point does this happen? Verify your answer by solving the two simultaneous equations given by his budget equation and the tangency condition. (2 pts) ?
g. What is Charlie’s utility if he consumes the bundle (20, 10)? On the graph, draw his indifference curve through (20,10). Does this indifference curve cross Charlie’s budget line, just touch it, or never touch it? (2 pts) ?

 

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