# Correct scientific term to describe this system property

I am from a non-economic background so please bare with me.

I have a crowdsourcing system that enables businesses to request individuals to perform certain tasks in exchange for a monetary payment. For any task t, the business pays an amount of p units as long as the participant is taking on only one task. If a user wishes to multi-task, the system pays an amount p-x where * x < p* and both are nonnegative. This motivates users to take on multiple tasks as it will achieve higher profitability to each user. At the same time, the incurred costs for businesses will be reduced. Is there a scientific term that describes this mechanism? Is the term "cost-efficiency" correctly describes what the business is trying to do?

• $p-x$ per task, or for all tasks? – Alecos Papadopoulos Oct 5 '17 at 11:04
• Per single task. So if a user takes on 3 tasks, he would be paid 3(p-x) instead of 3p – Rawan K-Something Oct 5 '17 at 12:29

The term is "volume discounting", where a supplier offers/accepts a lower unit price in exchange for higher volume of business. Here, it is the firm/buyer that asks for this volume discount, rather than the suppliers/users that offer it as a commercial policy.

Note that when the buyer demands a volume discount (when it sets $x$) some conditions must be satisfied in order to be even feasible. Assume $m$ tasks identical as regards the costs that the user has to incur (time etc). Denote the cost per task $c_a$.

For a single task the user is paid $p$, so its net payoff is $p-c_a$.

Taking on multitasking, the user will be paid in total $m\cdot (p-x)$ and its costs will be $m\cdot c_a$. In order to take on multitasking it must hold that

$$m\cdot (p-x-c_a) > p-c_a$$

A necessary but not sufficient condition for this to hold is that

$$p-x-c_a > 0 \implies x < p -c_a$$

which places an uper bound on $x$, a bound that depends on supplier costs $c_a$. So the firm/buyer that sets $x$ must have a good idea about what $c_a$ might be.

Assume that this holds. Then we need

$$m > \frac {p-c_a}{p-x-c_a}$$

The higher the reduction $x$ in price per task the more tasks a user must take on. This may seem like providing an incentive to the buyer to set the requested $x$ as bigger as possible, but it may be the case that the reduction in unit price is so large that the user cannot take on the necessary number due to physical constraints. Let a maximum possible number of tasks that the agent can hanlde be $\bar m$.

Then we need as a necessary condition

$$\frac {p-c_a}{p-x-c_a} < \bar m$$

so that there exist feasible number of tasks $m$ below the maximum, and above the minimum number required to have higher profitability of the supplier/agent.

Re-arranimng for $x$ we obtain

$$x< \left(1-\frac 1{\bar m}\right)(p-c_a)$$

which is tighter than the previous necessary condition on $x$. So the fimr/buyer must also have a good idea about what the value of $\bar m$ is. Otherwise the whole plan runs the risk of not being adopted by the user.

A situation where the above becomes more feasible is when $c_a$ is not fixed per task but at least initially declines with multi-tasking.

• Thanks a lot. I should mention that the maximum number of tasks that any user can take is predefined based on other system parameters, so the final equation is pretty straightforward to implement in the environment. – Rawan K-Something Oct 5 '17 at 13:52