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Abstract

The study investigates the economic response of tart cherry yields to planting density using an unbalanced longitudinal yield data from tart cherry orchards in Northwest Michigan. The relationship between tart cherry yield and tree age is specified as a linear spline function and planting density interacts with tree age. A random effect method, treating block as random, is used to estimate the spline function. Stochastic simulation was used to estimate the mean and variance of the product of two random variables (price and yield), and the coefficient of variation was used as a measure of how much risk is involved in corn/soybeans production relative to tart cherries production. Estimates of the variance provided the discount factor (10%) and with yields predicted from the statistical model, relevant cost data and prices, a deterministic simulation was performed to determine the economically optimal planting density, using annualized net present value (ANPV) as the decision-making criterion. Results of the study show that at a discount rate of 10% and tart cherries priced at $0.30 per lb, planting 160 trees per acre is most profitable. A sensitivity analysis is carried out to determine the effect of variation in interest rates and tart cherry prices on the optimal planting density. Changing the discount rate to 12% or 15% or the price to $0.50/lb did not change the most profitable planting density.

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