Intertemporal Utility Function

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Intertemporal preferences describe the way consumers make decisions between how much food they would consume today versus how much food they would consume tomorrow. The consumption of today would influence the consumption of food tomorrow. Some basic assumptions for intertemporal preferences are transitivity, consumer prefer more over less, and consumers can choose between two alternative streams (today versus tomorrow). A decision requires a trade off by the consumers between costs and benefits today and tomorrow. The more a consumer consumes today, the less saving he will have today which will result in less consumption tomorrow. When consumers make consumption decisions they have to take into account their future consumption of food. The intertemporal utility function is:
Utility function: u(c0,c1) = U(c0) + βU(c1)
Where β is the discount factor of the consumer on how much he discounts future consumption. When β is low, the consumer consumes most of the food today, and when β is high the consumer consumers most of the food tomorrow.
B. The intertemporal budget constraint refers to the fact that a consumer
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Next to that we assume that there is no chance in price level and the price of consumption is 1, which means that 1 euro extra of income leads to 1 extra unit of consumption. Consumption (C) and income (M) doesn’t need to be equal to each other in one period for the reason that a consumer can save or borrow money to increase his current or future consumption. We assume that consumers make decisions based upon present discounted value (PDV). In period 0 savings will equal to current income minus current consumption (equation 1) and in period 1 consumption will be equal to the further value (1+R) of the savings in period 0 and the current income of period 2, where R is the interest rate. We assume that the interest is the same for both

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