A company that produces software needs two inputs, programmers (L) whose wages are $2 and computers (K) with a price of $10. The output is given by Q = L1/3K1/3, measured in the codes written. Assume that the codes may be sold for a price of p = $4. 

(a) Check if the output function satisfy Young's theorem.

(b) Write the profit function.

(c) Find the levels of L and K that maximizes the profit function. Check for the set of SOCs.

2.

Consider the following utility function defined over two goods: 1 and 2: U(x1,x2) = x2/3x4/3. 12

The prices of goods 1 and 2 are p1 and p2 respectively.

(a) Does the law of diminishing marginal utility hold for good 2? Find the MRS of good 1

for good 2.

(b) Write the equation representing the budget constraint, assuming the consumer's income

is M.

(c) Using the method of Lagrange, maximize the utility subject to the budget constraint. What are the demand functions for x1 and x2. Assuming p1 = 2, p2 = 1 and M = 100, find the quantities of x1 and x2 that maximizes utility.

(d) Check the SOC for the Lagrangian method.