# Question 1 Consider a production function of the form: y = (x1 +23)=. Draw the isoquants and explain whether the technology is convex in the following cases: (a) When $

Question 1

Consider a production function of the form: y = (x1 +23)=. Draw the isoquants and explain whether

the technology is convex in the following cases:

(a) When $ = = [3.5 marks]

(b) When s = 2. [3.5 marks]

Question 2

Suppose a firm’s profit function is given by:

n (p, W1, (2) =

1 p3

9 w1 w/2

Compute the supply and input demand functions. Show the supply function slopes upwards and the

input demands slope downwards. Verify symmetry in cross-price effects. [8 marks]

Question 3

Suppose a firm has the following production function:

Y = (A+C)i Li

where A represents macbooks, C represents chromebooks and L denotes labor. The prices of the three

inputs are PA, pc and w. Solve for the conditional factor demands of each input and for the cost

function. [12 marks]

Question 4

Consider the following production function that uses labor (() and capital (k),

f ( e, k) = 202ki

Denote the price of labor by w and the price of capital by r. Suppose in the short-run the level of

capital the firm operates is fixed at k. In the long-run the firm can adjust both labor and capital.

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