Question

3. Nora enjoys fish (F) and chips(C). Her utility function is U(C, F) = 2CF. Her income is B per month. The price of fish is P_F and the price of chips is P_C. Place fish on the horizontal axis and chips on the vertical axis in the diagrams involving indifference curves and budget lines.

(a) What is the equation for Nora’s budget line?

(b) The marginal utility of fish is MU_F = 2C and the Marginal utility of chips is MU_C = 2F. What is the marginal rate of substitution of fish for chips? Is it constant? What is its geometric equivalent? What is its interpretation?

(c) Derive the equation for an indifference curve belonging to Nora.

(d) Draw a diagram which represents the choices available to Nora, her preferences over these choices, and her optimum choices. What conditions must be satisfied for utility maximization?

(e) Show that the demand function for fish is given by F = B/2P_F and the demand function for chips is given by B/2P_C. What information does a demand function impart? Is there anything unusual about these demand functions?

(f) What is the equation for the inverse demand function for fish? Draw this on a graph. If income increases, what would happen to the demand for fish? Illustrate this on a graph.

4. Nora, Part 2. Suppose that P_C = 100, P_F = 50, and B = 1,000. Place fish on the the horizontal axis and chips on the vertical axis in the diagrams involving indifference curves and budget lines.

(a) What is Nora’s optimal consumption bundle?

(b) Draw Nora’s budget line on a graph. Indicate her optimum consumption bundle. Verify that it is on the budget line. [The graph should be drawn to scale on a full sheet of graph paper. Please make it neat since you will be adding information to it in later parts.]

5. Nora, Part 3. Suppose P_F increases to 100.

(a) What is Nora’s new optimal consumption bundle? Draw her new budget line and indicate her new optimal consumption bundle in your diagram.

(b) What is the equation for the Marshallian demand curve for Fish?

(c) What is the equation for the Hicksian demand curve for fish?

(d). Determine the total effect, the substitution effect, and the income effect due to the change in P_F. What would Nora’s income have to be in order that her utility level is the same at the new prices as it was at the original prices? Show these answers on your graph.

5. Nora, Part 3. Suppose P_F increases to 100.

(a) What is Nora’s new optimal consumption bundle? Draw her new budget line and indicate her new optimal consumption bundle in your diagram.

(b) What is the equation for the Marshallian demand curve for Fish?

(c) What is the equation for the Hicksian demand curve for fish?

(d). Determine the total effect, the substitution effect, and the income effect due to the change in P_F. What would Nora’s income have to be in order that her utility level is the same at the new prices as it was at the original prices? Show these answers on your graph.

Answer 1

(a)

Budget line: B = F x PF + C x PC, where F, C: Quantity of fish & chips respectively

(b)

Marginal rate of substitution (MRS) = MUF/MUC = 2C/2F = C/F

Since values of C and F change as we move along indifference curve, MRS is not a constant all throughout the indifference curve.

Geometrically, MRS is the slope of the indifference curve, which specifies the number of units of chips that must be given up to consume one additional unit of fish.

(c)

U = 2CF

F = U / (2C) [Equation of indifference curve]

(d)

Utility-maximizing condition is: MRS = Price ratio, or (C/F) = PF/PC.

In following graph, utility is maximized at point X, where indifference curve IC0 is tangent to budget line AB with optimal quantity of chips being C* and of fish being F*.

NOTE: As per Answering Policy, 1st 4 parts are answered.