Question

Jon Snow consumes pizza and burgers. His utility function is u(P, B) = PB where P is the number of pizzas and B is the number of burgers. Jon Snow has $30 to spend, and he plans to spend it all on pizza and burgers. The price of one pizza is $10 and the price of one burger is $3.

(a) Find and label Jon Snow’s initial optimal bundle on a graph where pizza is on the x-axis and burgers are on the y-axis. Label this point A.

(b) Suppose that the local burger restaurant is running a promotion selling burgers at $2 a burger. Solve for Jon Snow’s new optimal bundle. Label this bundle B on your graph from part (a).

(c) Findthesubstitutioneffect,incomeeffect,andthetotaleffectforbothgoodsfollowing the decrease in the price of burgers from $3 to $2. Label the intermediate bundle used to find the substitution and income effects point C on your graph from part (a).

(d) Are pizza and burgers normal or inferior goods? Explain your answer.

Answer 1

The optimal bundle can be obtained by equating the MRS to the Price Ratio.

The total Price Effect can be decomposed into Substitution and Income Effect. Substitution Effect (SE)defines the effect of price change in isolation, excluding the effect of change in income. This can be calculated by hicksian approach or slutsky's approach. Hicksian approach calculates SE by calculating an intermediate bundle at which the utility is same as the original utility , at the new price level.

The income effect shows only the effect of change in real income alone.

The parts are solved as below and the diagram is provided at the end.

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Here the line passing through point C is the intermediate budget line drawn at the new price level but tangent to the original utility curve.