Suppose that you know the utility function for an individual is given by the equation U = XY where U is the total amount of utility the individual gets when they consume good X (X) and good Y (Y). Thus, if U = 10 then the individual can get 10 units of utility from consuming 1 unit of X and 10 units of Y (U = XY = (1)(10)) or from consuming 5 units of X and 2 units of Y or any other combination of X and Y whose product is equal to 10. Given this utility function, the MU from good X is equal to Y (that is, MUx = Y) and the MU from good Y is equal to X (that is, MUy = X). You are also told that this individual's income is $100 and that the price of good X is $2 and the price of good Y is $4. From this information answer the following set of questions. (40 Points)

a. What is the budget line for this individual given the above information?

b. What is the consumption bundle of good X and good Y that maximizes this individual's utility given their income, prices of the two goods, and their tastes and preferences as measured by their utility function?

c. Verify the answer you got in part (b) to make sure the individual can afford to buy this consumption bundle.

d. What is the level of utility this individual gets when they maximize their utility given the above information?.

1 Suppose Q units of output can be produced from funits of capital and h units of labour according to the following production function Q = 10KL. (i ) It can be shown that the marginal product of labour is 10K and the marginal product of capital (flour) is 10L. What is the marginal rate of technical substitution when 5 units of labour and 2 units of capital are used? (ii) If the price of labour is $30 per unit and the price of capital is $100 per unit, what is the minimum cost to produce 100 units of the output? What is the quantity of labour and capital used