Reference no: EM133313845

A chemical rm produces output according to the production function f(x) = 8√x, where x is electricity input. Output is sold in a competitive market at price $1 per unit, and electricity is purchased from the hydroelectric company at a price of $1 per unit. Assume the rm acts to maximize prots.

1. Formulate the rm's prot maximization problem. What is the optimal amount of electricity it will buy? (hint: You need to check the second order condition.)

2. Due to a drought, there is an electricity shortage. To cope with the crisis, the hydroelectric company announces the following scheme: if a user buys no more than 2 units of electricity, the price will be $1 per unit as before. However, for every unit of electricity purchased above this amount, there is an additional surcharge of $s. (Thus, for example, if the rm buys 6 units of electricity, it would have to pay a total of $2 for the rst 2 units, and $4(1+s)for the remaining 4 units). Assume that the price of output stays the same as before. Formulate the rms' prot maximization problem. What is the optimum amount of electricity the rm will buy if (i) s = 1, and (ii) s = 3?

3. What is the maximum prot it would make under the cases (i) and (ii) of (b) above?