Assume that Erica's preferences for wages and risk are given by the utility U =W x e-12R. Her friend Rambo's utility function is U = W x e-3R. Assume that W represents the hourly wage and that there is a range of job types within a particular firm, each having a different level of risk R. Erica's utility function implies that the slope of her indifference curve with respect to R (the MRS) is 12W. Rambo's MRS is 3W. The isoprofit for the firm is given as W = 60 x R (do not worry that the isoprofit is a straight line rather than a strictly concave curve).
Determine Erica's choice of wage and risk (algebraically).
Determine Rambo's choice of wage and risk. Sketch a diagram showing these choices.