Objective Function of Firm

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Objective function of firm: y-w-β+κ, for which β=ũy,κ=dka Production Function: y=ka
The objective function of firm has been added two functions based on the basic model, -β and +κ, showing the cost and the benefit of non monetary rewards respectively. They are allocated in the firm’s objective function, because the firm is the sender of the rewards, which the firm will have a cost and benefit of the reward from the worker. β is a negative function, since it is the cost of non monetary rewards or the opportunity cost foregone for the rewards to the firm. κ is a positive function; it is the benefit or the return to the firm when using non monetary rewards. It will show the immediate effect of increasing in workers’ effort and productivity after using the non monetary rewards. For example, workers will work harder when they know there is a reward for the best worker, even though it is in the period 1, which every worker do not know what the reward is, it is an immediate effect. κ will be relevant to β, the increase in β, an equal increase or a more increase in κ. This means they are in positive relationship.

Assume the firm will allocate some part of the revenue, y, to the workers as non monetary rewards. In this case, therefore, β would not be a constant, should be a variable. In reality, firm will choose to allot the some of the profit, y-w, but it will be too complicated to solve for the model, the revenue is preferred.

ũ is the percentage of the rewards measuring in monetary value, it is decided and observed by the firm. ũ ϵ N{0,1}. There is usually a cost to the firm when a non monetary reward given to workers, even a trophy or a certificate is a cost to the firm. This refers that the percentage of the costs of rewards may be very low.
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