4. ) For the following total revenue and total cost functions of a firm: TR=22Q-

Question

4. ) For the following total revenue and total cost functions of a firm: TR=22Q-0.5Q^2 , TC= 1/3Q^3- 8.5Q^2+50Q+90

4a) Determine the level of output at which the firm maximizes its total profit.

4b) Determine the maximum profit that the firm could earn.

5) A firms total-revenue and total-cost functions are, TR=4Q , TC= 0.04Q^3-0.9Q^2+10Q+5

5a) Determine the best level of output.

5b) Determine thw total profit of the firms at its best level of output.

6.) Given the following cost function, determine the level of (nonzero) output at which the costfunction is minimized, and the level of the costs. AC= 200-Q^2

7.) Given the following cost function, determine the level of (nonzero) output at whic the cost function is minimized, and the level of the costs. MC=200-48Q+3Q^2

9) The Warren & Smith Company manufactures commercial zippers of two kinds, kind X and kind Y. Its production department estimates that the average-cost function of the firm is: AC=X^2+2Y^2-2XY-2X-6Y+20

9a) The manager of the firm would like to know the level of output of zipper X and zipper Y at which the average cost of the firm is minimized, and the level of this minimum average cost.

9b) The firm expects an order that will require it to produce a total output of 6 units of both kinds of zippers (each unit may be a large numberof zippers), and so the manager would also like to know how many of each type of zipper the firm must produce to minimize its average cost, and what its minimum average cost would be if it receives the order. The manager gives this assignment to two researchers who use different methods to obtaintheir answers.

10.) EViews: Given the Coffee price and quantity data, develop each of the items 2 - 4 requested above.

1.) Develop the Group Descriptive statistics, copy and paste into MS Word Assignment 3 document and interpret the results,

2.) Using the group, develop a Scatter Diagram of the two series, copy the Scatter Diagram graph, paste into your MS Word Assignment 3 document, and interpret the results.

3.) Develop the group correlation matrix, copy the matrix and paste in MS Word document and interpret results

Explanation / Answer

4 a) Total revenue and total cost functions of a firm: TR=22Q-0.5Q^2 , TC= 1/3Q^3- 8.5Q^2+50Q+90.

The profit maximising condition of firm is,

MR=MC

We need to find out MR=dTR/dy=22-Q.

MC=dTC/dy=Q2-17Q+50.

Following the profit maximising condition we have,

MR=MC

Or,22-Q=Q2-17Q+50

Or,Q2-16Q+28=0

Or,Q2-(14+2)Q+28=0

Or,Q2-14Q-2Q+28=0

Or,Q(Q-14)-2(Q-14)=0

Or,(Q-14)(Q-2)=0

OrQ=14 orQ=2

b)Putting value of Q we get profit like-

Profit=TR-TC

=-1/3Q3+8Q2-28Q-90

=-914.67+1568-392-90

=1568-(914.67+392+90)

=1568-1396.67

=171.33

Putting Q=2 we have

TR-TC

=-2.67+32-56-90

=32-(56+90+2.67)

=32-148.67

=-116.67=This is not profit it is loss.

So the maximum profit that firm can earn is 171.33.

5 a)TR=4Q , TC= 0.04Q^3-0.9Q^2+10Q+5

MR=4=P

MC=.12Q2-1.8Q+10

Profit maximising condition,

P=MC

Or,4=.12Q2-1.8Q+10

Or,.12Q2-1.8Q+6=0

Or,12Q2-180Q+600=0

Or,Q2-(10+5)Q+50=0

Or,Q2-10Q-5Q+50=0

Or,(Q-10)(Q-5)=0

Or,Q=10 or 5.

b)Putting value of Q we have,

4Q-.04Q3-.9Q2-10Q-5

=40-40-90-100-5

=-195here is loss

4Q-.04Q3-.9Q2-10Q-5

=20-5-22.5-50-5

=-62.5 here is also loss.

So the minimum loss is -62.5.

6.) Given the following cost function, determine the level of (nonzero) output at which the costfunction is minimized, and the level of the costs. AC= 200-Q^2-

To determine the level of output at which cost function will be minimised we need to do derivative of the cost function,

dAC/dQ=2Q=0

Or,Q=0

d2AC/dQ2=2>0

So Q=0 is the critical point.As second order condition is greater than 0 so cost function must be minimum at that point.

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