Question

1. A political candidate has D dollars worth of donations. The candidate can spend money on either media M (which costs PM per unit) or events E (which cost PE per unit). The total number of votes for the candidate is based on the function V (M, E) = ME. The candidate is trying to maximize their votes, subject to their budget D.

a) What is the objective function for this problem?

b) What is the constraint?

c) Which of the variables, {E, V, D, PM, M, PE}, are exogenous? Which are endogenous? Explain.

d) Write a complete statement of the constrained optimization problem.

Answer 1

According to the question,

Candidate wants to maximize the number of votes which is dependent on the value function.

a) The objective function for this problem: Maximise V(M,E) = ME

b) Constraint: M*PM + E*PE =D

where PM is the cost per unit spend on M, PE is the cost per unit spend on E and D dollars worth of donations. The candidate can't spend more than D.

c) Exogenous variables: Variables that are given in the model, not determined by the model. In our given set up, prices PM and PE, as well as budget D, are already given.

Endogeneous variables: Variables that are determined by the model or within the model by other (exogenous) variables. In our given set up, units of M and E, as well as Value function V, will be determined by or are dependent on the other variables.

d) The constrained optimization problem is the method of optimizing (maximizing or minimizing) the objective function given constraints. According to the question:

Maximise V(M,E) = ME

subject to M*PM + E*PE =D

M>=0

E>=0