Michelle produced 400 units of high-quality olive oil at a constant marginal cost of c = 50 per unit. She is trying to decide how much of her fixed supply to sell this year (year 1) or next year (year 2). She knows that demand in any given year is given by pt = 500 qt and is interested in her marginal profit, pt c , not just the price. Michelle is extremely impatient and uses a discount rate of 50 percent a) Write down an equation that describes the equilibrium relationship between marginal profits in year 1 and year 2. b) Use part (a) and the demand in each period to calculate the optimal quantity of olive oil to sell in year 1 and year 2. c) Use part (b) and the demand in each period to calculate the optimal price of olive oil in year 1 and year 2. d) Calculate the present value of Michelle's profits over the two years.