Economics 10A: Problem Set 1
Economics经济代写 You have $10 to spend on goods A and B. The budget constraint is 2A – B = 10, assuming non-negative values for A and B.
(1) Solve for the partial derivative with respect to x and y for the following functions. Note that letters other than x and y are constants. Economics经济代写
U(x,y) = xayb
U(x,y) = 5y ln x
U(x,y) = 5x + 2y
U(x,y) = 20x – x2 + 18y – 3y2
(2) You have $40 to spend on two commodities. Good 1 (x1) and good 2 (x2).
(a) What is the equation for the budget constraint if the price of good 1 is $10 and the price of good 2 is $5?
(b) What are the intercept and the slope if this is graphed in (x1,x2) space? (c) Is the slope steeper or flatter is the price of good 2 rises to $10?
(3) The budget constraint is 2x + 4y = 20. Economics经济代写
(a) Draw this budget constraint in (x,y) space.
(b) How much of good y can you afford if you spend all your money on good y? (c) How much of good x can you afford if you spend all your money on good x?
(d) At what rate can you trade good x for good y and remain on the budget constraint?
(4) You have $10 to spend on goods A and B. The budget constraint is 2A – B = 10, assuming non-negative values for A and B.
(a) Draw this budget constraint in (A,B) space.
(b) Mark the affordable region and the unaffordable regions.
(c) Is this a sensible budget constraint? Does it make any sense? Would we ever see such a budget constraint?