#2c. Suppose we want to simulate a profit function where there is one output, in amount x, and two inputs, in amounts y1 and y2. We sell the output for $10/unit. Input 1 costs $3/unit but we are uncertain about the cost of input 2. We know the cost of input 2 is normally distributed with a mean of $3/unit and a standard deviation of $1/unit, then what Excel equation would we use to represent the cost of input 2? #2d. The notes for Chapter 11 presented a simulation of the Single Index Model from finance. This model is basically an application of the simple regression model y = b0 + b1x + e, where e is a normal random variable with mean 0 and some finite standard deviation. What Excel equation would we use to simulate a normal random variable with mean 0 and standard deviation of 0.05? #1c. Suppose we want to simulate a profit function where there is one output, in amount x, and two inputs, in amounts y1 and y2. We sell the output for $10/unit. Input 1 costs $3/unit but we are uncertain about the cost of input 2. We know the cost of input 2 will be between $2/unit and $4/unit. If we assume the cost of input 2 is uniformly distributed, then what Excel function would we use to represent the cost of input 2? #1d. The notes for Chapter 11 presented a pro forma forecast of the total liabilities and equity for a firm by using a simple sales growth model. To do so, we assumed the growth rate was a uniform random variable between 5% and 7%. What Excel function would we use to represent a uniform growth rate between 3% and 9%? 5. Consider the following payoff table (where the payoffs are measured in dollars). Value State 1 State 2 Act 1 16 1 Act 2 0 81 Probabilities .6 .4 The modestly risk averse decision maker uses the square root utility function, i.e., U(x) = x 0.50 = sqrt(x). Which act would the modestly risk averse decision maker choose? (Show your work.)