Consider a firm with a production function: , where l is employment and y is output. The good is sold at price p and the hourly wage is equal to w. First, we consider the environment certain .

a) Recall what are the values of the demand for work, the proreduction and maximum profit of the company. They will be denoted , and

It is now assumed that the producer has to deal with uncertainty about the selling price. It just knows that the price is random, that its average value is and its variance

b) Recall the interpretation of the variance.

c) It is assumed that the entrepreneur is risk neutral (maximizes the expected gain). Determine the demand for labor, the supply of goods, and the maximum profit. They will be denoted , and . What is the variance of profit in this case?

d)How does the production of an uncertain universe compare to that of a certain universe?

We assume that the entrepreneur admits Markowitz preferences: U() = E() kV().

e) Recall the interpretation of parameter k. When do we have a risk-phobic entrepreneur? risk-loving?

f) Determine the demand for labor, the supply of goods and the maximum profit. They will be denoted ,and .

g) How do these three quantities vary with price volatility, risk aversion?