Question

1. a. Sam allocates his monthly lunch budget between lunch boxes and salad bowls. Write down his utility function and the equation of his budget line. What is the slope of his budget line, if salad bowels are on the horizontal axis? If he uses all of his monthly lunch budget on salad bowls, what is the maximum number of salad bowls he could purchase?

b. Following the above question, draw a budget line and then draw an indifference curve to illustrate Sam’s satisfaction-maximizing choice associated with two lunch options.

2. a. Nickels and dimes are perfect substitutes. Draw the indifference curves that represent your preferences for them, with dimes on the vertical axis, and nickels on the horizontal axis.

b. Are the slopes of the indifference curves positive or negative?

c. The slope of an indifference curve measures the consumer’s marginal rate of substitution (MRS) between two goods. Is MRS constant in the graph you draw? (correctly answering this question, 1 pt) What is the economic meaning behind the MRS, or the slope of the indifference curve, for two perfect substitutes? (explain the economic meaning of MRS, in a way that is reasonable, 3 pts)

3. If the demand for ice cream in the summer is written as Q = 8 – 5P, then what is the inverse demand function?

Answer: (Hint: write P at the left hand side of the equation, as a function of Q)

4. Consider the market of TV screens. Suppose a technological advance reduces the cost of manufacturing TV screens. Draw a graph to show what happens in the market of TV screens.

Answer 1

1.

a.

Let X = quantity of lunch boxes

Y = quantity of salad bowls

Utility Function of Sam is given by:

where = Budget proportion spent on lunch box

= 1 - alpha = Budget Proportion spent on salad bowl

Equation of budget line:

X*Px + Y*Py = M

M = Income

Slope of the budget line = Price ratio = -Py/Px

Max number of salad bowls if the entire budget is spent on it = M / Py

In this case, X = 0

So, from budget line,

0*Px + Y*Py = M

Y = M/Py

b.

Indifference curve is convex to origin IC1. BC1 denotes the budget line of the consumer in the graph below. Refer to figure 1.b.

Point A shows maximizing bundle which is given by the tangency between IC1 and BC1

2.

a.

Let Nickels = N and Dimes = D

The Indifference curves are downward sloping straight lines. IC1 and IC2. Refer to figure 2.a.

b.

The slope of the indifference curve is Negative.

c.

Yes, MRS is constant on the Indifference Curve.

Constant MRS in this cases implies that the consumer is willing to give X quantity of one good to gain an Y additional quantity of the other good where X = Y

3.

Q = 8 – 5P

5P = 8 - Q

P = 1.6 - 0.2Q ; Inverse demand function

4.

Initial equilibrium is at point E where supply and demand curves intersect. Due to technological advancement, the supply curve shifts to right. Equiibrium price decrease from P to P1 and quantity increases from Q to Q1

Refer to Figure 4

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