### Exploring Profit Maximizing Output <!-- -->To run this page correctly, you need a more modern browser that understands JavaScript.<P><!--Beginning of JavaScript function checkanswer() { //var f=document.question; w=0;r1=0; r2=0; r3=0; if (f.mc3.value==4.){f.A.src=imaged[2].src;} else {f.A.src=imaged[3].src;w++} if ((f.ac4.value>=5.6) && (f.ac4.value<=5.7)){f.B.src=imaged[2].src;} else {f.B.src=imaged[3].src;r1++} if (f.profit4.value==9.5){f.C.src=imaged[2].src; } else {f.C.src=imaged[3].src;r2++} if (f.profit.selectedIndex==5){f.D.src=imaged[2].src; } else {f.D.src=imaged[3].src;r3++} a1="Very good." if (r3==1) a1="d) The easiest way to find where profits are maximized is to compute marginal costs first. Then ask, is it worth producing the first? Yes, because revenue goes up by \$8 and cost only be \$4. Then do the same for the second, etc. "; if (r2==1) a1="c) To find the profit at 4, you need to know the total revenue. But each of the 4 added \$8.00 to revenue. So what is total revenue? From it, subtract \$22.50."; if (r1==1) a1="b) To find the average cost of four, divide the total cost of four, \$22.50, by 4."; if (w==1) a1="a) When two are produced, total cost is \$13. When three are produced, total cost is \$17. By how much did costs go up when the third was produced? That is the marginal cost of the third unit."; f.comment.value=a1; } function check() { //var f=document.question; w1=0; w2=0; w3=0; a2="Very Good!"; if (f.profit2.selectedIndex==5){f.G.src=imaged[2].src; } else {f.G.src=imaged[3].src;a2="You want to keep producing as long as MR is greater than MC. And not beyond.";} if (f.mr1.value==15) w2++; if (f.mr2.value==15) w2++; if (f.mr3.value==15) w2++; if (f.mr4.value==15) w2++; if (f.mr5.value==10) w2++; if (f.mr6.value==8) w2++; if (w2==6){f.F.src=imaged[2].src;} else {f.F.src=imaged[3].src; a2="How can you miss the marginal revenues when you got total revenues right? MR is just the change in TR.";} if (f.tr1.value==15) w1++; if (f.tr2.value==30) w1++; if (f.tr3.value==45) w1++; if (f.tr4.value==60) w1++; if (f.tr5.value==70) w1++; if (f.tr6.value==78) w1++; if (w1==6){f.E.src=imaged[2].src;} else {f.E.src=imaged[3].src; a2="People can only pay \$15 because of the price ceiling. So replace any number that is above 15 in column 3 with 15, and multiply it by output to get total revenue.";} f.comment2.value=a2; } //-End of JavaScript- -->

2. Use the following table for the next four questions:

 OUTPUT TOTAL COST MARGINAL REVENUE Marginal Cost. Total Revenue Profit 0 \$5 -- -- 1 (first) \$9.00 \$8.00 2 (second) \$13.00 \$8.00 3 (third) \$17.00 \$8.00 4 (fourth) \$22.50 \$8.00 5 (fifth) \$30.00 \$8.00

a) What is the marginal cost of the third unit of output? \$

b) What is the average cost of four units of output? \$

c) What is profit or loss when output is 4? \$

d) Where are profits maximized?

3. The table of the reading (reproduced below) showed a seller maximizing profit at three units of output. Suppose that the government puts a price ceiling of \$15 on this seller.

 Computation of the Best Output for the Firm (1) Output (2) Total Cost (3) Price (that people are willing to pay) (4) Total Revenue (5) Which Output (5) Marginal Revenue (6) Marginal Cost 0 \$10 -- -- -- -- 1 \$20 \$18 \$ First \$ \$10 2 \$31 \$17 \$ Second \$ \$11 3 \$43 \$16 \$ Third \$ \$12 4 \$56 \$15 \$ Fourth \$ \$13 5 \$70 \$14 \$ Fifth \$ \$14 6 \$85 \$13 \$ Sixth \$ \$15

a) Recompute the total revenue and marginal revenue columns of the table. (Hint: What is the highest price the seller can charge if it sells only one unit? If it sells six units? Be careful.)

What is the profit-maximizing level of output with the price ceiling?

c) Using supply and demand curves, we showed that price ceilings reduced output. However, the price ceiling in this problem is not reducing output. What is going on? (Hint: Check the section on supply and demand for assumptions on the number of buyers and sellers needed for supply and demand curves.)

4. a) Suppose there are 30 people in a room with the average age of 40 years. A 15-year-old boy walks in and the average age of the group becomes 40.5. Is this possible?
b) A firm is producing 30 units of output at an average cost of \$40. Adding another unit will increase costs by \$15 (this is the marginal cost) and the average cost will rise to \$40.5. Is this possible?
c) If average cost is falling, what must be true of marginal cost?