Question

Two firms X and Y produce the same commodity. Due to production constraints, each firm is
able to produce 1, 3 and 5 units. The cost of producing x q units for firm X is
` [6+ q square(x)-2q(x)+ 5] and firm Y has identical cost function ` [6_+ q square(y) -2q(y) + 5] 2 + − + y y q q for producing
y q units. p is the price of one unit for firm X . We assume that the market is in equilibrium.
The outcomes are the profits of the firm shown in the form of a matrix A = {aij } . Write (i) a11
(ii) a22 (iii) a21, if demand function D( p) is given as D( p) = 50 − p .

Answer 1

Solution:

$$Pr=TR-TC$$

$$TR=pQ$$

$$x+y=50-p$$

$$p=50-(x+y)$$

$$TR=(x+y)(50-(x+y))$$

$$TC=TC(x)+TC(y)$$

For $a_{11}$ x=1 and y=1

$$Pr=2\times 48 - 20=96-20=76$$

For $a_{22}$ x=3 and y=3

$$Pr=6\times44-28=236$$

For $a_{21}$ x=3 and y=1

$$Pr=4\times46-21=163$$