The accounting department of a large firm is interested in modeling the dynamic of its accounts receivable (that is, the money that is owed to it by its customers) when a charge sale occurs, abill is sent out at the end of the month. payment is due within thirty days, but may not occure in that time. if no payment is received within six months of the billing date, the amount is classified as bad debt. thus, an individual account is described by its age in months, or by "paid" or by "bad debt". For numerical values, assume that the prob. that payment is made in the first month is 0.8 and decline by 0.1 each additional month. that is, the prob. it is paid in the second month is 0.7, in the third month is 0.6, and so on. Formulate the terminating Markov chain that describes the debt payment.

Question

Elaina Buchanan

Business

16 June, 02:50

The accounting department of a large firm is interested in modeling the dynamic of its accounts receivable (that is, the money that is owed to it by its customers) when a charge sale occurs, abill is sent out at the end of the month. payment is due within thirty days, but may not occure in that time. if no payment is received within six months of the billing date, the amount is classified as bad debt. thus, an individual account is described by its age in months, or by "paid" or by "bad debt". For numerical values, assume that the prob. that payment is made in the first month is 0.8 and decline by 0.1 each additional month. that is, the prob. it is paid in the second month is 0.7, in the third month is 0.6, and so on. Formulate the terminating Markov chain that describes the debt payment.

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Thalia Hammond · Answer 1

Here is the Markov chain, when the problem says 'terminating' it means that the probability after seven months never changes. After six months

accounting moves it to "bad debt," and, for the purposes of this problem, transistion probabilites end.

Month one: paid 0.8 unpaid 0.2

Month two: paid 0.7 unpaid 0.3

Month three: paid 0.6 unpaid 0.4

Month four: paid 0.5 unpaid 0.5

Month five: paid 0.4 unpaid 0.6

Month six: paid 0.3 unpaid 0.7

Month seven: and above paid 0 unpaid 1.0