(a) If I=1000, p_y=10 and utility is given by u=x+2y^1/2, find the income and substitution effects of an increase in the price of x from $5 to $10.

(b) Suppose the production function is Q=4K^1/2L. Find the conditional demands for K and L and the cost function, and show that Shephard's Lemma holds for this cost function (and show only Shephard's Lemma, not the other properties!).

(c) The only way to produce 1 unit of output for a particular good is to use 2 machines (K) AND 4 workers (L). Show the production function, the MRTS, and the cost function for this technology, then show this cost function exhibits the 4 properties of all cost functions.