ECON301(01)
ECON301 2021W
Dr. Yuan
Assignment 2
Assignment 2 is due on March 10, 2021 at 11:30 PM. The file should be submitted in the Dropbox in D2LYou are encouraged to work in groups, but each person must submit his or her own answers. Please do not write more than is required in the question; show your work; and check your spelling. NO LATE ASSIGNMENTS WILL BE ACCEPTED. All questions should be answered, with the answers in order.
XXXXXXXXXXmarks) The utility function is given by: u(x, y) = (xy)10 and the original budget is x+2y=100, where Px=1 and Py=2. Then the price of x goes up to 4.
(a) Find the demand function of x.
(b) Find demand elasticity when Px changes from 1 to 4.
(c) Find the substitution effect, income effect, and total change in demand for good x as defined in the lectures.
(d) Illustrate the changes in (c) with a graph.
(e) Find the EV.
2. (30 marks) Given Q=2x1/2+y1/2. P, Wx, and Wy are prices for output, input x, and input y respectively. MPx= x-1/2 and MPy=1/2 y-1/2.
(a) Illustrate by example that the technology implies diminishing marginal products for input x.
(b) Show that the technology exhibits decreasing return to scale.
(c) Write out the isoquant equation for Q=100 (express y as a function of x) and illustrate it in a graph.
(d) In the short run, y=400. Find the short run demand function of x and the supply function of Q.
(e) Find the long run demand function of x and supply function of Q.
3. (40 marks) Consider a production function for a firm:
Q = 2K1/2L1/2
where Q is output, K is capital, and L is labor. MPK= K-1/2L1/2 and MPL= K1/2L-1/2. Suppose initially K is equal to 25 units and L is equal to 16 units. You also know that the price of K, Pk, is $10 per unit of K and the price of L, Pl, is $4 per unit of L.
a. Given the above information, what is the value of output?
. What is the total cost of producing the output you calculated in (a)?
c. What is the average total cost of producing this level of output?
d. What is the marginal revenue product of K? Can you tell whether K=25 maximizes the profit? Why?
e. What the MRT?
f. Suppose the amount of labor increases to 32 units and the amount of capital increases to 50 units. Given this information, what level of output can the firm now produce? (Hint: you can do this without a calculator – and, then you can check your answer with a calculator!)
g. Given the information in (f), what is the total cost for the firm of producing this level of output?
h. Given the information in (f) and (g), calculate the firm’s average total cost of producing this new level of output.
i. Given your answer to the above set of questions, what can you conclude about returns to scale for this firm?
h. Find the optimal input bundle for Pk=10 and Pl=4.