Adrienne and Sarah consume pizza, \(Z\), and cola, \(C\). Adrienne's utility function is \(U_{A}=Z_{A} C_{A}\), and Sarah's is \(Z_{D}^{0.5} C_{D}^{0.5}\). Adrienne's marginal utility of pizza is \(M U_{A}^{Z}=C_{A}\). Similarly, \(M U_{C}^{A}=Z_{A}, M U_{Z}^{D}=\) \(\frac{1}{2} Z_{D}^{-0.5} C_{D}^{0.5}\), and \(M U_{C}^{D}=\frac{1}{2} Z_{D}^{0.5} C_{D}^{-0.5}\). Their endowments are \(Z_{A}=10, C_{A}=20, Z_{D}=20, C_{D}=10\).

a. What are the marginal rates of substitution for each person?

b. What is the formula for the contract curve? Draw an Edgeworth box and indicate the contract curve. A