Question

14. Use the production matrix presented to answer the following questions. ܗ ܨ ܗ ܕ 27 23 17 12 6 3 1 101 183 99122 B2 108 69 91 54 72 38 54 24 33 11 17 3 4 62 54 45 34 25 14 7 2 161 147 130 108 89 65 44 27 5 ܛܝ ܟ 184 168 149 126 101 74 54 19 6 202 184 168 137 108 79 47 16 7 213 193 163 142 111 7 9 48 8 8 ܟܬ ܝܕ X a. Determine the returns to scale for this matrix. (Start with one unit of X and one unit of Y.) b. Suppose the firm has a budget of $100, and the price of Y is $20 and the price of Xis $10. What is the optimal combination of inputs X and Y for this firm? - Sunnose the prices of Yand X are now $10 and $20, respectively. What effect will this help?

Answer 1

14)

a) From the production matrix: looking at the diagonal values, representing the (X,Y) such that (X= Y).

When we are employing (1,1) output = 3,

At (2,2) total output = 14

At (3,3) total output = 38.

Thus when the input are increased two times the total output increases more than two time. Thus the increasing returns to scale exist.

b) Budget = $100.

10X + 20Y =100

X	Y	Total Output
2	4	34
4	3	54
6	2	54
8	1	8
At this given budget and price level of inputs X and Y: Two options are available (X=4, Y = 3) and (X = 6, Y =2), where total output is maximised and equals 54