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.

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

18 Värdet på en aktie steg på några år från 65 kr till 150 kr. a) Med hur många kronor steg värdet? b) Med hur många procent steg värdet? Avrunda till tiotal.

A store sells \( Q \) units of a product per year. It costs \( d \) dollars to store one unit for a year. To reorder, there is a fixed cost of b dollars, plus c dollars for each unit. How many times per year should the store reorder, and in what lot size, in order to minimize inventory costs? Use the general solution to find how many times per year a store should reorder, and in what lot size, when \( Q=100, d=\$ 10, b=\$ 20 \), and \( c=\$ 14 \).

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.)

\( 1<\begin{array}{l}\text { Suppose someone wants to accumulate } \$ 50,000 \text { for a college fund over the next } 15 \text { years. Determine whether the } \\ \text { following investment plans will allow the person to reach the goal. Assume the compounding and payment periods } \\ \text { are the same. } \\ \text { The person deposits } \$ 80 \text { per month into an account with an APR of } 7 \% \text {. } \\ \text { Will the person meet the goal? Select the correct choice below and fill in the answer box to complete your choice. } \\ \text { (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places } \\ \text { as needed.) } \\ \text { A. No, because the amount that will be in the college fund, } \$ \square \text {, is less than the goal of } \$ 50,000 \text {. } \\ \text { B. Yes, because the amount that will be in the college fund, } \$ \square \text {, is more than the goal of } \$ 50,000 \text {. }\end{array} \).