You are developing the strategy for a new product, namely production and marketing. On the production side, if you hire a worker with skill level s, they will require an hourly wage w(s). Working for h hours, the worker will produce f(h,s) units of the product. Marketing generates product appeal. The more appealing the product, the higher the price you can charge: with appeal a, you can set a price of p(a) per unit. To achieve appeal a, your marketing cost will be m(a).

a) Do you expect w (s) to be positive or negative? Justify your answer with economic intuition.

b) Write the total profit function in terms of the variables a,s, h

c) How would you find the optimal strategy for a,s, h? (Someone should be able to do so by following your steps exactly.)

d) Pick one of the first order conditions and relate it to the concepts of marginal revenue and cost.

Now suppose workers will only work on the product if they are motivated to afterwards, they will lose interest. The maximum number of hours they will stay motivated depends on their skill level and the appeal of the product according to g(a,s).

e) Express the above as an inequality constraint

f) Describe how you would find the best product strategy.