Question

Utilizing the following Christmas Tree production function that you had completed in Homework 2 that includes output and cost information for a firm, respond to the questions given, assuming the firm is a perfectly competitive firm:

Input (Units of Water)	Output (Christmas Trees)	MPP	TFC	TVC	TC	AFC	AVC	ATC	MC
0	0		4500	0	4500
10	70	7	4500	3500	8000	64.29	50.00	114.29	50.00
20	145	7.5	4500	7000	11500	31.03	48.28	79.31	46.67
30	220	7.5	4500	10500	15000	20.45	47.73	68.18	46.67
40	290	7	4500	14000	18500	15.52	48.28	63.79	50.00
50	345	5.5	4500	17500	22000	13.04	50.72	63.77	63.64
60	395	5	4500	21000	25500	11.39	53.16	64.56	70.00
70	440	4.5	4500	24500	29000	10.23	55.68	65.91	77.78
80	480	4	4500	28000	32500	9.38	58.33	67.71	87.50
90	515	3.5	4500	31500	36000	8.74	61.17	69.90	100.00
100	545	3	4500	35000	39500	8.26	64.22	72.48	116.67

a.) Assume that the selling price for Christmas Trees is $80/tree. What would be the approximate profit-maximizing rate of output that you would want to produce? Would the firm be generating profit above all costs at that selling price? Why or Why not?

b.)If the price of Christmas Trees drops to $60/tree, approximately how many trees would now be produced for the optimum level? Are you making a profit above all costs at $60/tree? Why or Why not?

c.)At what price would be the short-run break-even point? At what price would be the firm’s short-run shutdown point?

Answer 1

Answers:-

(A)

440 trees should be produced because in a perfect competitive firm maximize profit when the output level which P=MC. The closest to $80 without going over on the table .At this rate, 440 trees will be produced.

=> ATC=$65.91 and Profit = (P-ATC)Q = (80-65.91)440 =$6,199.6

=> so yes the firm will generate profit because the price is greater than the Average total cost

(B)

=> Doing the same thing in figure a, the closest Marginal cost to $60 without going over is $50. At the MC, 290 trees will be produced. ATC=$63.79 (60-63.79)290 =-$1,099.1. So here this number is negative it is a loss but not a profit so the price is less than the ATC.

(C)

At a breakeven point, the total revenue is equal to Total cost. TR=TC or ATC=P or P=MC so MC=ATC.

We seen from the table that the output rate where MC is almost the same to ATC. When there is an output of 345 then ATC=$63.77 and MC=$63.64 so the output breakeven is 345. The breakeven price is $64