Problem: Consider a market with many identical consumers that consume two types of goods, Education, E, and other goods, X. Assume that education is a composite good given by E = E(e1,e2,…ek), where e1,e2,…ek are different education goods purchased by the individual (i.e. public school, private school, tutoring, parental time, etc.) and that utility is given by U(X,E).
A. How would you measure the price of the composite good, E? In particularhow would you measure the price of E in order to tell whether the individual is better or worse off from a change in educational input prices?
B. Would an increase in the price of education as measured in part A lead the individual to consume more X and less E as long as real income was unchanged by the price change?
C. Can you construct a price index on consumption goods that would generate the result that E will decrease as the price index for E increased?
What information do we need in order to construct such an index?
D. Could a subsidy on one educational input, such as public schooling, paid for by a tax on X reduce the individuals’ consumption of E even if it did not reduce real income?
E. Derive the Hicksian demand parameters for the inputs e1,e2,…ek in terms of the Hicksian demand for the composite good E and the technology for combining inputs into the aggregate E?