Question

Part III. Graphing the perfectly competitive model (20 points). Use one graphing paper only for the graph. Attach the graphing paper with this completed questionnaire upon submission. All answers should be handwritten. Given: Selling price P=60 Total cost TC = 128 +69 Q-14 Q2 +Q? 1. Average cost equation AC= 2. Marginal cost equation MC = 3. Fill in the blanks in the table. You should be able to show that at the optimum rate of output, Q*, the profit is at its maximum and that MR = MC. Total Total | Profit Marginal Marginal Average | Average | Average revenue cost revenue cost revenue cost variable cost 10 11 12 Note: Instead of the slope formula, get the exact values of MC using the equation above. 4. Figure 1: Graph the total revenue (TR) and total cost (TC) curve. Label the maximum profit corresponding to the optimum rate of output, Q* 5. Figure 2: Graph the average revenue (AR), average cost (AC), marginal revenue (MR) and marginal cost (MC) curves. Label the maximum profit and the total cost corresponding to Q*.

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Answer 1

Ans 1.)

Average cost = Total Cost ÷ Q

= (128 + 69Q - 14Q² + Q³) ÷ Q

  

Average cost = (128/Q) + 69 - 14Q + Q²

Ans.2)

Marginal Cost = d(TC)/d(Q)

= 69 - 28Q + 3Q²

Ans 3.)

In the above image, we can see that the profit is maxmized at output leve = 9th unit.Also , at this level, profit is maximum = $196.

Output Price Total revenue Marginal revenue Marginal Cost Average revenue Average cost Average variable cost 0 Profit -128 -124 60 184 109 120 -98 -56 79 180 240 300 61 Total cost 128 184 218 236 244 248 254 268 296 344 418 524 50 EEBOO vou A WNHO 360 106 420 480 540 600 152 184 196 182 136 660 720 668 52

So, the optimum level of output = 9 units

Ans 4.)

0 1 2 3 4 5 6 7 8 9 10 11 12 Total revenue Total cost

In the above image, we can see that the profit is maximized at a point where the gap between the total cost and total revenue curve is highest , as indicated by red colored line.