Question 1 Mpho is a utility maximizing consumer. Her Cobb Douglas Utility function is given by \[ U(X, Y)=X^{\frac{1}{4}} Y^{\frac{3}{4}} \] (a) Derive the Marshallian demand curves for good \( X \) and \( Y \). (b) (i) Derive the indirect utility function (ii) Derive the expenditure function from (b) (i). (iii) Derive the Hicksian demand curve for good \( X \). (iv) Why are these demand curves termed compensated demand curves? (c) You are given that the price of \( X, P_{x} \) is R 15 , whilst the price of \( Y, P_{y} \) is R 45 . The consumer's budget M is fixed at \( \mathrm{R} 540(M=540) \). (i) Use the Marshallian demand curves from (a) to find the values of \( X \) and \( Y \). (ii) Compute and comment on Mpho's marginal rate of substitution.

Qual das seguintes afirmaçōes geralmente não pode ser correta para um investidor que tem responsabilidade ilimitada sobre um investimento: \( \begin{array}{l}\text { a. O investidor não tem sócio } \\ \text { b. O investidor é responsável pelo } \\ \text { gerenciamento da empresa. } \\ \text { d. O investidor está sujeito a dupla taxaçāo } \\ \text { d. } 0 \text { investidor possui acçōes na empresa }\end{array} \)

anual ¿Cual fue sl capital inicial con el que se hizo el deposit? Tengo un pagare por \( \$ 200000 \) que vence en 40 dias, cuanto dinero obtendria hoy si lo cambio, sab ido que la tasa es del \( 40 \% \) anual

3. Mika opened a bank account that earns simple interest with an initial deposit of \( \$ 2,200 \). She made no other transactions throughout the year. At the end of the year, Mika had \( \$ 2,260.50 \) in her account. What was the simple interest rate?

A college foundation raises funds by selling 600 raffle tickets for a new car worth \( \$ 46,000 \) at \( \$ 140 \) each. (a) Find the expected net winnings of a person buying one of the tickets. (b) Find the total profit for the foundation, assuming they had to purchase the car. (c) Find the total profit for the foundation, assuming the car was donated. (a) The expected net winnings are \( \$-63.33 \). (Round to the nearest hundredth as needed.) (b) Assuming they had to purchase the car, the total profit for the foundation is \( \$ \) (Simplify your answer.)

3) Después de 3 años, un banco ha pagado en concepto de inter s's la cantidad de \( \$ \) 840 a una persona por depositar un plazo fijo La tasa de inter's ha sido del \( 2 \% \) anual ¿Cual fue ol capital inicial con el que se hizo el deposi?