Suppose the utility function for two goods, X and Y, has the

Cobb-Douglas utility form:

U(X; Y ) = pXY

a. Graph the U = 10 indierence curve associated with this

utility function.

b. If X = 5; what must Y equal to be on the U = 10 indierence

curve? What is the MRSX;Y at this point?

c. In general, develop an expression for the MRSX;Y for this

utility function. Show how this can be interpreted as the ratio of

the marginal utilities for X and Y .

d. Consider a logarithmic transformation of this utility function:

U0 = log U

where log is the logarithmic function to base 10. Show that for this

transformation the U0 = 1 indierence curve has the same proper-

ties as the U = 10 curve calculated in parts (a) and (b). What is

the general expression for the MRSX;Y of this transformed utility

function?.

Kindly help!

Question 5. [4 marks] If Farmer Brown plants no seeds on his farm, he gets no harvest. If he plants 1 bag of seeds, he gets 5 bushels of wheat. If he plants 2 bags, he gets 9 bushels. If he plants 3 bags, he gets 12 bushels. A bag of seeds costs $120, and seeds are his only cost. a. Is Farmer Brown's marginal-cost curve increasing, decreasing or constant? Explain b. What is Farmer Brown's marginal cost of producing 9 units of output (using 2 bags of seed)? Question 6. [3 marks] Suppose a firm is using 1500 units of labour and 20 units of capital to produce 100 tonnes of mineral ore. The price of labour is $50 per unit and the price of capital is $800 per unit. What is the total cost of producing 100 tonnes of mineral ore?1. (30 pts) Suppose Saul consumes two goods, r and y, which have the prices pr = py = 4, and she has an income m = 360, all in TLs, to spend on these two goods only. Suppose that the utility he gets from a bundle b = (c, y) is given by u(x, y) = k ln(x) + 2y, where k > 0. (a) (12 pts) At the given prices and income levels, find Saul's demand for a and y, as a function of k. (b) (12 pts) Suppose Saul picks a corner bundle with only a in it at the prices p, = py = 4 and income level m = 360. Suppose also that at the prices p', = 6 and p', = 2 and income level m = 360, he picks an interior bundle. Find a range for & values that is consistent with this given information. (c) (6 pts) Suppose k = 240. Find Saul's Engel curve y(m), when prices are pr = 6 and p,, = 2