Galaxy co. distributes wireless routers to internet service providers. galaxy procures each router for $75 from its supplier and sells each router for $125. monthly demand for the router is a normal random variable with a mean of 100 units and a standard deviation of 20 units. at the beginning of each month, galaxy orders enough routers from its supplier to bring the inventory level up to 100 routers. if the monthly demand is less than 100, galaxy pays $15 per router that remains in inventory at the end of the month. if the monthly demand exceeds 100, galaxy sells only the 100 routers in stock. galaxy assigns a shortage cost of $30 for each unit of demand that is unsatisfied to represent a loss-of-goodwill among its customers. management would like to use a simulation model to analyze this situation.

a. what is the average monthly profit resulting from its policy of stocking 100 routers at the beginning of each month?
b. what percentage of total demand is satisfied?

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?