microeconomics

microeconomics

2. We have a profit function π : 3p (ln(3p/ w)-1) , where p is the product price, y, and w is the price of the supplies, x.

a) Find the supply function of the product and demand for the supplies. (Hint: you use Hotelling’s lemma) Is it possible to set up the production function of the product? If so, do that.

b) See if the profit function meets the properties of the profit-functions. Justify the results.

You can find those properties here: https://www.colorado.edu/economics/morey/6808/profit-function.pdf

Solution Preview

2a. For supply;

      We partially differentiate the profit function with respect to product price (p) while treating price of the supplies (w) as a constant;

       3p[ln(3p/w) – 1]

      We apply product rule;

     d/dp = 3p * (1/p) + 3 * [ln(3p/w) – 1]

     d/dp = 3 + 3* [ln(3p/w) – 1]

       Therefore supply function = 3 * [1 + (ln(3p/w) – 1)]

(318 words)