Question

1)Indifference curves and budget constraints:

(a)Explain how you would mathematically figure out and give a verbal interpretation of both intercepts and the slope of the budget constraint.

(b)Explain why the slope of the budget constraint is a constant but the slope of the indifference curve decreases as you move to the right along the X axis (have more X and less Y)

(c)If MRS>Px/Py, explain why this would happen, why this would cause the consumers to change their bundle, and how they make this change? Show this graphically

(d)If MRS<Ps/Py, explain why this would happen, why this would cause the consumer to change their bundle, and how they make this change? Show this graphically

2)Substitution and Income effect:

(a)On a graph using standard convex indifference curves and a linear budget constraint, graphically show and explain the income and substitution caused by an increase in the price of the good on the x axis.

(b) Graphically show and explain the income and substitution caused by and decrease in the price of the good on the x axis.

(c)In each above, explain why the old bundle of goods before the price change the equilibrium bundle after the price change is no longer.

(d)Referring to and based on your answers in a) and b) above, explain (1) whether X and /or Y are normal or inferior good and (2) whether X and Y are compliments or substitutes.

3)Demand

(a)On a graph with standard convex indifference curves and linear budget constraint, derive the demand curve for the good on the Y axis (note: you need a set of indifference curves and a set of budget constraints to do this). Make sure you clearly indicate the prices and quantities in both graphs.

(b)On both graphs used above, for the change in price, show the income effect and the substitution effect.

(c)For the demand curve, certain things are held constant-what are they and show how this approach holds them constant (use the graph to help you explain what is held constant)

(d)Explain what is not being held constant or can change using this approach.

Answer 1

1.a. The equation of budget constrain is as follows:

M = Px * X + Py. Y.

Where M is the income of the consumer.

The budget line is plotted as a downward sloping straight line. With good Y on the vertical axis and the good X on the horizontal axis. At the vertical intercept, value of X is zero. So all the income would be spent on good Y, maximum amount can be purchased is = M/Py.

Similarly, at horizontal intercept, the value of Y is zero. So all the income would be spent on good X, maximum amount can be purchased is = M/Px.

For slope, re-arranging the budget equation, M = Px * X + Py. Y

M - Px * X = Py * Y

Y = M/Py - Px * X/Py

Thus, slope of budget line is -Px/Py.

b. Clearly, as seen above, the slope of the budget line is the price ratio of the two goods. Since the price of the goods do not change, so the slope also does not vary.

The slope of the indifference curve is the marginal rate of substituion of x and y. As the consumer consumes more of x and less of y, the marginal utility derived from x would start falling and that from the y would start rising. This would alter the slope of the indifference curve.

c. MRSx,y = MUx/MUy.

So if, MUx/MUy > Px/Py, then by just simple cross multiplication,

MUx/Px > MUy/Py will also hold true. This means that marginal utility from consuming x is more than y. The consumer would be willing to have more X in his bundle than Y, and he would be moving to downward to the right on his IC.

b. USing the same logic as above, MUx/Px < MUy/Py.  This means that marginal utility from consuming y is more than x. The consumer would be willing to have more Y in his bundle than X, and he would be moving to upward to the left on his IC.